CUET UG Applied Mathematics Booster Test 2 - Interest Rates and Compound Annual Growth Rate (CAGR) -

🚀

CUET UG Applied Mathematics Booster Test 2 - Interest Rates and Compound Annual Growth Rate (CAGR)

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Applied Mathematics Booster Test 2 - Interest Rates and Compound Annual Growth Rate (CAGR)

1 / 20

QUESTION 1 OF 20

Mohan takes a loan of ₹5,00,000 at an 8% flat annual interest rate for 6 years. What is the total interest ((I)) calculated before EMI?

Answer Review

1 Mohan takes a loan of ₹5,00,000 at an 8% flat annual interest rate for 6 years. What is the total interest ((I)) calculated before EMI?

A ₹2,00,000

B ₹2,40,000

C ₹3,00,000

D ₹1,50,000

💡 Short Explanation

Under the flat-rate method, interest is calculated on the original principal. Use the simple interest formula. The total interest is ₹2,40,000.

✅ Correct Answer Explanation

The flat-rate interest formula is I = P × r × t where P = ₹5,00,000 r = 8% = 0.08 t = 6 years Substituting, I = 5,00,000 × 0.08 × 6 = 2,40,000 Therefore, I = ₹2,40,000 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: ₹2,00,000
Incorrect because it underestimates the interest.
Option C: ₹3,00,000
Incorrect because it exceeds the calculated value.
Option D: ₹1,50,000
Incorrect because it is much lower than the correct interest.

🎯 Strategy

used

Substitution

Application:

Apply the flat-rate interest formula directly.

Final Logic:

Since
5,00,000 × 0.08 × 6 = 2,40,000
Option B is correct.

🧠 Memory Trick

"Flat Interest = Principal × Rate × Time."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Flat Rate Interest

2 What is the effective rate of interest if the nominal rate is 8% compounded quarterly?

A 8.00%

B 8.16%

C 8.12%

D 8.24%

💡 Short Explanation

Quarterly compounding means four compounding periods. Use the effective interest rate formula. The effective rate is 8.24%.

✅ Correct Answer Explanation

The effective annual rate is iₑₓₓ = (1 + r/m)ᵐ − 1 where r = 0.08 m = 4 Thus, iₑₓₓ = (1 + 0.08/4)⁴ − 1 = (1.02)⁴ − 1 = 1.082432 − 1 = 0.082432 Therefore, iₑₓₓ ≈ 8.24% Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 8.00%
Incorrect because it is only the nominal rate.
Option B: 8.16%
Incorrect because it is lower than the effective rate.
Option C: 8.12%
Incorrect because it underestimates the quarterly compounded rate.

🎯 Strategy

used

Substitution

Application:

Apply the effective interest rate formula.

Final Logic:

Since
(1.02)⁴ − 1 = 8.24%
Option D is correct.

🧠 Memory Trick

"Quarterly Effective = ((1+r/4)^4-1)."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Effective Interest Rate

3 To what amount will ₹12,000 accumulate in 12 years if invested at an effective rate of 5%?
(Use \({1.05}^{12}\approx 1.7958\))

A ₹21,550

B ₹22,000

C ₹19,500

D ₹24,000

💡 Short Explanation

Use the compound amount formula. Multiply the principal by the compound growth factor. The accumulated amount is approximately ₹21,550.

✅ Correct Answer Explanation

The compound amount formula is A = P(1 + i)ⁿ where P = ₹12,000 i = 5% = 0.05 n = 12 Substituting, A = 12,000 × 1.7958 = 21,549.6 Rounding, A ≈ ₹21,550 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹22,000
Incorrect because it is higher than the calculated value.
Option C: ₹19,500
Incorrect because it underestimates the compound amount.
Option D: ₹24,000
Incorrect because it exceeds the calculated amount.

🎯 Strategy

used

Substitution

Application:

Use the compound amount formula with the given growth factor.

Final Logic:

Since
12,000 × 1.7958 ≈ 21,550
Option A is correct.

🧠 Memory Trick

"Amount = Principal × Growth Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Compound Interest Formula

4 What is the effective rate equivalent to a nominal rate of 10% compounded semi-annually?

A 10.00%

B 10.50%

C 10.25%

D 10.15%

💡 Short Explanation

Semi-annual compounding means interest is compounded twice a year. Apply the effective interest rate formula. The effective annual rate is 10.25%.

✅ Correct Answer Explanation

The effective annual rate is iₑₓₓ = (1 + r/m)ᵐ − 1 where r = 0.10 m = 2 Substituting, iₑₓₓ = (1 + 0.10/2)² − 1 = (1.05)² − 1 = 1.1025 − 1 = 0.1025 Hence, iₑₓₓ = 10.25% Therefore, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: 10.00%
Incorrect because it is the nominal rate.
Option B: 10.50%
Incorrect because it overestimates the effective rate.
Option D: 10.15%
Incorrect because it is below the calculated value.

🎯 Strategy

used

Substitution

Application:

Apply the effective interest rate formula for semi-annual compounding.

Final Logic:

Since
(1.05)² − 1 = 10.25%
Option C is correct.

🧠 Memory Trick

Semi-annual ⇒ (1 + r/2)² − 1

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Effective Interest Rate

5 The effective rate for a continuous compounding nominal rate of 9.5% is given by
\(e^{0.095}-1\). If \(e^{0.095}=1.0996\), find the effective rate.

A 9.50%

B 9.75%

C 10.00%

D 9.96%

💡 Short Explanation

Continuous compounding uses the exponential function. Subtract 1 from the exponential value. The effective rate is 9.96%.

✅ Correct Answer Explanation

For continuous compounding, iₑₓₓ = eʳ − 1 Given, e^0.095 = 1.0996 Therefore, iₑₓₓ = 1.0996 − 1 = 0.0996 Converting to percentage, iₑₓₓ = 9.96% Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 9.50%
Incorrect because it is the nominal rate.
Option B: 9.75%
Incorrect because it is less than the calculated effective rate.
Option C: 10.00%
Incorrect because the effective rate is slightly below 10%.

🎯 Strategy

used

Substitution

Application:

Use the continuous compounding formula directly.

Final Logic:

Since
1.0996-1=0.0996,
the effective rate is 9.96%, so Option D is correct.

🧠 Memory Trick

Continuous Effective = (e^r − 1)

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Continuous Compounding

6 Between 10% compounded semi-annually and 9.5% compounded continuously, what is the effective rate of the continuous option specifically?

A 10.25%

B 9.96%

C 9.50%

D 10.00%

💡 Short Explanation

Only evaluate the continuously compounded investment. Use the continuous compounding formula. The effective annual rate is 9.96%.

✅ Correct Answer Explanation

The effective rate under continuous compounding is iₑₓₓ = eʳ − 1 Here, r = 9.5% = 0.095 Using, e^0.095 = 1.0996 we obtain, iₑₓₓ = 1.0996 − 1 = 0.0996 = 9.96% Therefore, 9.96% Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 10.25%
Incorrect because it is the effective rate of the 10% semi-annual investment.
Option C: 9.50%
Incorrect because it is the nominal rate.
Option D: 10.00%
Incorrect because it is not the calculated effective rate.

🎯 Strategy

used

Substitution

Application:

Evaluate only the continuously compounded option.

Final Logic:

Since
e^0.095 − 1 = 9.96%
Option B is correct.

🧠 Memory Trick

"Continuous ⇒ (e^r-1), not the nominal rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Comparison of Interest Rates

7 Compare an 8% effective rate and 7.8% compounded semi-annually. What is the effective rate of the 7.8% semi-annual option?

A 7.95%

B 8.00%

C 7.80%

D 8.12%

💡 Short Explanation

Convert the nominal rate into an effective annual rate. Semi-annual compounding means two compounding periods. The effective rate is approximately 7.95%.

✅ Correct Answer Explanation

The effective annual rate is iₑₓₓ = (1 + r/m)ᵐ − 1 where r = 0.078 m = 2 Substituting, iₑₓₓ = (1 + 0.078/2)² − 1 = (1.039)² − 1 = 1.079521 − 1 = 0.079521 Therefore, iₑₓₓ ≈ 7.95% Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: 8.00%
Incorrect because it is the effective rate of the other investment.
Option C: 7.80%
Incorrect because it is the nominal rate, not the effective rate.
Option D: 8.12%
Incorrect because it exceeds the calculated value.

🎯 Strategy

used

Substitution

Application:

Convert the nominal rate into its effective annual equivalent.

Final Logic:

Since
(1.039)² − 1 ≈ 7.95%
Option A is correct.

🧠 Memory Trick

"Effective Rate is always slightly higher than the nominal rate."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Effective Rate of Interest

8 What is the exact mathematical difference in the effective rate between 10% compounded semi-annually and 9.5% compounded continuously?

A 0.50%

B 0.15%

C 0.29%

D 0.75%

💡 Short Explanation

Compute both effective rates. Find their difference. The difference is 0.29%.

✅ Correct Answer Explanation

For 10% compounded semi-annually, i₁ = (1 + 0.10/2)² − 1 = 10.25% For 9.5% compounded continuously, i₂ = e^0.095 − 1 = 9.96% Therefore, Difference = 10.25% − 9.96% = 0.29% Thus, 0.29% Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: 0.50%
Incorrect because it overestimates the difference.
Option B: 0.15%
Incorrect because it is too small.
Option D: 0.75%
Incorrect because it is much larger than the actual difference.

🎯 Strategy

used

Direct Comparison

Application:

Calculate both effective rates and subtract one from the other.

Final Logic:

Since
10.25%-9.96%=0.29%,
Option C is correct.

🧠 Memory Trick

"Difference = Effective Rate₁ − Effective Rate₂."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Comparison of Effective Interest Rates

9 The revenue of a company is ₹3,00,000 in 2015 and ₹3,50,000 in 2016. What is the exact one-year growth rate?

A 15.00%

B 16.67%

C 14.47%

D 18.00%

💡 Short Explanation

Calculate the increase in revenue. Divide the increase by the original revenue. The one-year growth rate is 16.67%.

✅ Correct Answer Explanation

The annual growth rate is Growth Rate = ((EV − SV) / SV) × 100% Given, SV = ₹3,00,000 EV = ₹3,50,000 Thus, Growth Rate = ((3,50,000 − 3,00,000) / 3,00,000) × 100 = (50,000 / 3,00,000) × 100 = 16.67% Therefore, 16.67% Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 15.00%
Incorrect because it underestimates the growth.
Option C: 14.47%
Incorrect because it is unrelated to this one-year calculation.
Option D: 18.00%
Incorrect because it overestimates the increase.

🎯 Strategy

used

Percentage Increase Formula

Application:

Subtract the starting value from the ending value and divide by the starting value.

Final Logic:

Since
(50,000 / 3,00,000) × 100 = 16.67%
Option B is correct.

🧠 Memory Trick

"Growth % = Increase ÷ Original × 100."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Annual Growth Rate

10 If ₹20,000 is invested for 5 years at a CAGR of 11.84% (Ending Value = ₹35,000), what is the total accumulated interest?

A ₹15,000

B ₹20,000

C ₹35,000

D ₹11,840

💡 Short Explanation

Total accumulated interest equals the ending value minus the starting value. Subtract the principal from the accumulated amount. The accumulated interest is ₹15,000.

✅ Correct Answer Explanation

The accumulated interest is Interest = EV − SV where SV = ₹20,000 EV = ₹35,000 Substituting, Interest = 35,000 − 20,000 = 15,000 Therefore, Interest = ₹15,000 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹20,000
Incorrect because this is the original investment.
Option C: ₹35,000
Incorrect because this is the ending value.
Option D: ₹11,840
Incorrect because it is the CAGR percentage expressed as an amount.

🎯 Strategy

used

Direct Subtraction

Application:

Subtract the initial investment from the ending value.

Final Logic:

Since
35,000-20,000=15,000,
Option A is correct.

🧠 Memory Trick

"Interest = Ending Value − Starting Value."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR and Investment Returns

11 An investment starts at ₹2,000 and grows for 3 years at a CAGR of 108%. What is the ending value?

A ₹16,000

B ₹20,000

C ₹15,000

D ₹18,000

💡 Short Explanation

Use the CAGR formula for ending value. Multiply the starting value by the compound growth factor. The ending value is ₹18,000.

✅ Correct Answer Explanation

The compound growth formula is EV = SV(1 + r)ⁿ where SV = ₹2,000 r = 108% = 1.08 n = 3 Thus, EV = 2,000(2.08)³ Since, (2.08)³ ≈ 8.9989 ≈ 9 we obtain, EV = 2,000 × 9 = 18,000 Therefore, EV = ₹18,000 Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹16,000
Incorrect because it underestimates the compounded value.
Option B: ₹20,000
Incorrect because it exceeds the calculated value.
Option C: ₹15,000
Incorrect because it is below the actual ending value.

🎯 Strategy

used

Substitution

Application:

Substitute the values into the CAGR formula.

Final Logic:

Since
2,000(2.08)³ ≈ 18,000
Option D is correct.

🧠 Memory Trick

"Ending Value = Starting Value × Growth Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR Formula (Ending Value)

12 An investment yields ₹25,000 in 4 years with a CAGR of 49.53%. What is the starting value?

A ₹10,000

B ₹7,500

C ₹5,000

D ₹2,500

💡 Short Explanation

Rearrange the CAGR formula to find the starting value. Divide the ending value by the compound growth factor. The starting value is ₹5,000.

✅ Correct Answer Explanation

The CAGR formula is EV = SV(1 + r)ⁿ Therefore, SV = EV / (1 + r)ⁿ Given, EV = ₹25,000 r = 49.53% = 0.4953 n = 4 Since, (1.4953)⁴ ≈ 5 we obtain, SV = 25,000 / 5 = 5,000 Therefore, SV = ₹5,000 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: ₹10,000
Incorrect because it would produce an ending value of approximately ₹50,000.
Option B: ₹7,500
Incorrect because it gives a larger ending value than ₹25,000.
Option D: ₹2,500
Incorrect because it gives a much smaller ending value.

🎯 Strategy

used

Rearrangement of Formula

Application:

Rearrange the CAGR formula to calculate the initial investment.

Final Logic:

Since
25,000 / (1.4953)⁴ = 5,000
Option C is correct.

🧠 Memory Trick

"Starting Value = Ending Value ÷ Growth Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR Formula (Starting Value)

13 Investment P yields 10% compounded semi-annually. Investment Q yields 9.5% compounded continuously. What is the numerical difference in their effective rates?

A 0.29%

B 0.50%

C 0.15%

D 0.75%

💡 Short Explanation

Compute the effective annual rate of each investment. Subtract one effective rate from the other. The difference is 0.29%.

✅ Correct Answer Explanation

For Investment P, iₚ = (1 + 0.10/2)² − 1 = (1.05)² − 1 = 10.25% For Investment Q, i_Q = e^0.095 − 1 Given, e^0.095 = 1.0996 therefore, i_Q = 1.0996 − 1 = 9.96% Hence, Difference = 10.25% − 9.96% = 0.29% Thus, 0.29% Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: 0.50%
Incorrect because the actual difference is smaller.
Option C: 0.15%
Incorrect because it underestimates the difference.
Option D: 0.75%
Incorrect because it greatly overestimates the difference.

🎯 Strategy

used

Direct Comparison

Application:

Calculate both effective annual rates and subtract them.

Final Logic:

Since
10.25%-9.96%=0.29%,
Option A is correct.

🧠 Memory Trick

"Compare Effective Rates, not Nominal Rates."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Comparison of Effective Interest Rates

14 A stock is bought at ₹100 and sold after 2 years at a CAGR of 22.47%. What is the exact selling price?

A ₹122

B ₹135

C ₹145

D ₹150

💡 Short Explanation

Use the CAGR formula for ending value. Multiply the purchase price by the compound growth factor. The selling price is ₹150.

✅ Correct Answer Explanation

The CAGR formula is EV = SV(1 + r)ⁿ where SV = ₹100 r = 22.47% = 0.2247 n = 2 Thus, EV = 100(1.2247)² Since, (1.2247)² ≈ 1.50 we obtain, EV = 100 × 1.50 = 150 Therefore, EV = ₹150 Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: ₹122
Incorrect because it represents only one year's growth.
Option B: ₹135
Incorrect because it underestimates compound growth.
Option C: ₹145
Incorrect because it is below the calculated value.

🎯 Strategy

used

Substitution

Application:

Apply the CAGR formula to compute the ending value.

Final Logic:

Since
100(1.2247)² ≈ 150
Option D is correct.

🧠 Memory Trick

"Selling Price = Purchase Price × Growth Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR Applications

15 A company's sales grow by 10% in Year 1, decrease by 5% in Year 2, and grow by 10% in Year 3. What is the simple Average Annual Growth Rate (AAGR)?

A 4.50%

B 6.00%

C 5.00%

D 5.50%

💡 Short Explanation

AAGR is the arithmetic average of annual growth rates. Add the yearly rates and divide by the number of years. The AAGR is 5.00%.

✅ Correct Answer Explanation

The AAGR formula is AAGR = (Sum of Annual Growth Rates) / (Number of Years) Substituting, AAGR = (10 + (−5) + 10) / 3 = 15 / 3 = 5% Therefore, AAGR = 5.00% Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: 4.50%
Incorrect because it is below the arithmetic average.
Option B: 6.00%
Incorrect because it overestimates the average.
Option D: 5.50%
Incorrect because it is not the arithmetic mean.

🎯 Strategy

used

Arithmetic Mean

Application:

Add the annual growth rates and divide by the total number of years.

Final Logic:

Since
(10 − 5 + 10) / 3 = 5%
Option C is correct.

🧠 Memory Trick

"AAGR = Sum of Annual Rates ÷ Number of Years."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Average Annual Growth Rate (AAGR)

16 Using the same data (10%, −5%, 10%), ₹100 grows sequentially to ₹114.95. What is the 3-year CAGR based on
\(\left(1.1495)^{1/3},\ 1\right.\)?

A 5.00%

B 4.75%

C 5.25%

D 4.50%

💡 Short Explanation

CAGR measures the constant annual growth rate. Use the CAGR formula based on the overall growth factor. The CAGR is approximately 4.75%.

✅ Correct Answer Explanation

The CAGR formula is CAGR = (EV / SV)^(1/n) − 1 Here, EV / SV = 114.95 / 100 = 1.1495 and n = 3 Therefore, CAGR = (1.1495)^(1/3) − 1 ≈ 0.0475 = 4.75% Thus, CAGR ≈ 4.75% Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 5.00%
Incorrect because it is the arithmetic average (AAGR), not the CAGR.
Option C: 5.25%
Incorrect because it overestimates the compound growth.
Option D: 4.50%
Incorrect because it underestimates the compound growth.

🎯 Strategy

used

Substitution

Application:

Use the CAGR formula with the overall growth factor.

Final Logic:

Since
(1.1495)^(1/3) − 1 ≈ 4.75%
Option B is correct.

🧠 Memory Trick

"CAGR uses the overall growth factor, not the average of yearly rates."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR vs AAGR

17 Over 4 years, a company's customer base expands from 53,000 to 1,05,000. Calculate the exact numeric ratio
\(\frac{EV}{SV}.\)

A 1.5000

B 1.8639

C 1.9811

D 2.0500

💡 Short Explanation

Divide the ending value by the starting value. This gives the total growth multiplier. The ratio equals 1.9811.

✅ Correct Answer Explanation

The growth ratio is EV / SV = 1,05,000 / 53,000 Therefore, EV / SV = 1.9811 Thus, EV / SV = 1.9811 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A: 1.5000
Incorrect because it underestimates the actual growth.
Option B: 1.8639
Incorrect because it is below the calculated ratio.
Option D: 2.0500
Incorrect because it overestimates the ratio.

🎯 Strategy

used

Direct Division

Application:

Divide the ending value by the starting value.

Final Logic:

Since
105000 ÷ 53000 = 1.9811
Option C is correct.

🧠 Memory Trick

"Growth Ratio = Ending Value ÷ Starting Value."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Growth Ratio

18 If the CAGR of a market index is 14.47% over 3 years starting from a base of ₹3,00,000, what is the final index value?

A ₹4,50,000

B ₹4,44,000

C ₹4,60,000

D ₹4,30,000

💡 Short Explanation

Apply the compound growth formula. Multiply the starting value by the growth factor. The final index value is ₹4,50,000.

✅ Correct Answer Explanation

The CAGR formula is EV = SV(1 + r)ⁿ where SV = ₹3,00,000 r = 14.47% = 0.1447 n = 3 Since, (1.1447)³ ≈ 1.5 we obtain, EV = 3,00,000 × 1.5 = 4,50,000 Therefore, EV = ₹4,50,000 Hence, Option A is correct.

❓ Why Other Options Are Incorrect

Option B: ₹4,44,000
Incorrect because it is lower than the calculated value.
Option C: ₹4,60,000
Incorrect because it exceeds the calculated amount.
Option D: ₹4,30,000
Incorrect because it underestimates the compounded growth.

🎯 Strategy

used

Substitution

Application:

Use the CAGR formula to compute the ending value.

Final Logic:

Since
3,00,000(1.1447)³ ≈ 4,50,000
Option A is correct.

🧠 Memory Trick

"Ending Value = Starting Value × Growth Factor."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR Applications

19 An investment grows uniformly at a CAGR of 11.84% for 5 years. What is the multiplier factor
\(\left(\frac{EV}{SV}\right)?\)

A 1.50

B 1.75

C 2.00

D 1.25

💡 Short Explanation

The multiplier factor represents the ratio of Ending Value to Starting Value. Use the CAGR growth formula. The multiplier is 1.75.

✅ Correct Answer Explanation

The multiplier is given by EV / SV = (1 + r)ⁿ where r = 11.84% = 0.1184 n = 5 Substituting, EV / SV = (1.1184)⁵ ≈ 1.75 Therefore, EV / SV ≈ 1.75 Hence, Option B is correct.

❓ Why Other Options Are Incorrect

Option A: 1.50
Incorrect because it underestimates the compounded growth.
Option C: 2.00
Incorrect because it overestimates the multiplier.
Option D: 1.25
Incorrect because it is much smaller than the calculated value.

🎯 Strategy

used

Substitution

Application:

Use the CAGR multiplier formula
(1 + r)ⁿ

Final Logic:

Since
(1.1184)⁵ ≈ 1.75
Option B is correct.

🧠 Memory Trick

Multiplier = (1 + CAGR)ⁿ

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: CAGR Multiplier

20 If an asset's value increases from ₹15,000 to ₹25,000 over 6 years, what is the annualized compound growth rate (CAGR)?

A 7.50%

B 9.15%

C 8.50%

D 8.88%

💡 Short Explanation

CAGR is the constant annual growth rate that converts the starting value into the ending value. Apply the CAGR formula. The annualized growth rate is 8.88%.

✅ Correct Answer Explanation

The CAGR formula is CAGR = (EV / SV)^(1/n) − 1 Given, SV = ₹15,000 EV = ₹25,000 n = 6 First, calculate the growth ratio: EV / SV = 25,000 / 15,000 = 1.6667 Now, CAGR = (1.6667)^(1/6) − 1 ≈ 0.0888 Therefore, CAGR ≈ 8.88% Hence, Option D is correct.

❓ Why Other Options Are Incorrect

Option A: 7.50%
Incorrect because it underestimates the compound annual growth.
Option B: 9.15%
Incorrect because it is slightly higher than the calculated CAGR.
Option C: 8.50%
Incorrect because it is below the calculated value.

🎯 Strategy

used

Substitution

Application:

Use the CAGR formula with the given starting value, ending value, and time period.

Final Logic:

Since
(25,000 / 15,000)^(1/6) − 1 ≈ 8.88%
Option D is correct.

🧠 Memory Trick

"CAGR = Root of Growth Ratio − 1."

📚 Class XII – Applied Mathematics – Chapter: Financial Mathematics – Topic: Compound Annual Growth Rate (CAGR)

CUET UG Applied Mathematics Booster Test 2 - Interest Rates and Compound Annual Growth Rate (CAGR)

Test Complete!

Answer Review