Statistics & Applications

Financial Math

Medium

applied

Ram had invested Rs. 15,000 in a mutual fund and the value of the investment at the time of redemption was Rs. 25,000. If the compound annual growth rate (CAGR) is 8.88%, then the number of years for which Ram has invested the amount is:

[Given: $\log 1.089 \approx 0.0370$ and $\log 1.667 \approx 0.2220$ ]

6 years

5 years

7 years

4 years

✅ Correct Option: 1

The initial investment is Rs. 15,000 and the final value is Rs. 25,000. The CAGR is 8.88% per year.

The compound annual growth rate formula is:

$A = P(1 + r)^n$

where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate, and $n$ is the number of years.

Substituting the values:

$25,000 = 15,000 × (1 + 0.0888)^n$

$25,000 = 15,000 × (1.0888)^n$

Dividing both sides by 15,000:

$\dfrac{25,000}{15,000} = (1.0888)^n$

$\dfrac{5}{3} = (1.0888)^n$

$1.667 = (1.0888)^n$

Taking logarithm on both sides:

$\log(1.667) = \log(1.0888)^n$

$\log(1.667) = n × \log(1.0888)$

Since $1.0888 \approx 1.089$ , using the given values:

$0.2220 = n × 0.0370$

$n = \dfrac{0.2220}{0.0370}$

$n = 6$

Therefore, Ram invested for 6 years.

2025: 15 May Shift 1

Which of the following is not the specification of the Sinking Fund?

2025: 27 May Shift 1

A person has set up a sinking fund in order to have Rs. 10,00,000 after 10 years for his child education. The amount should put bi-annually into account paying 5% per annum compounded semi-annually is: [Given $(1.025)^{20} = 1.6386$ ]

2025: 30 May Shift 1

The scrap value of a machine costing ₹ 75,000 after 4 years of use is ₹ 25000. Using straight line method the annual depreciation of the machine is:

2025: 21 May Shift 1

Which of the following statements are correct?

(A) In the sinking fund a fixed amount at regular intervals is deposited.

(B) Sinking fund is a long-term account which can be closed any time.

(D) Sinking fund can be used only for the purpose it was created.

Choose the correct answer from the options given below:

2025: 15 May Shift 2

Which of the following are similarities between the sinking fund and the savings account?

(A) The sinking fund and the savings account are both financial tools.

(B) Both can be used in any emergency.

(D) Both are long-term accounts which can be closed any time.

Choose the correct answer from the options given below:

2026: 26 May Shift 2

Harish invested ₹ 40,000 in a no-fee fund. After one year, the value of the fund rose to ₹ 60,000 then the nominal rate of return on the investment is

Solution

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