Arithmetic

Simple & Compound Interest

Medium

If a certain sum becomes three times in 4 years at compound interest, then in how many years, will it become 9 times?

✅ Correct Option: 3

Let the principal amount be $P$ and the growth factor be $(1 + r)$ where $r$ is the rate of interest.

Using the compound interest formula:

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

When the amount becomes 3 times in 4 years:

$3P = P(1 + r)^4$

$3 = (1 + r)^4$

For the amount to become 9 times after $n$ years:

$9P = P(1 + r)^n$

$9 = (1 + r)^n$

Notice that $9 = 3^2$ :

$9 = 3^2$

$9 = [(1 + r)^4]^2$

$9 = (1 + r)^{4 \times 2}$

$9 = (1 + r)^8$

Comparing $9 = (1 + r)^n$ with $9 = (1 + r)^8$ :

$n = 8$

Therefore, the amount will become 9 times in 8 years.

2023: 15 June Shift 2

Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what will Rs. 800 amount to in 3 years:

2025: 13 May Shift 1

Arrange the simple interest of the following cases in decreasing order-

(A) The simple interest on Rs 6600 at 5% per annum for 2 yrs.

(B) The simple interest on Rs 200 at 6% per annum for 5 yrs.

(D) The simple interest on Rs 5000 at 12% per annum for 2 yrs.

Choose the correct answer from the options given below:

2022: 17 Aug Shift 1

The interest earned on $\rupee 25000$ in 5 years at simple interest is $\rupee 1500$ . What is the rate of interest?

2024

A certain sum becomes ₹ 2,356 in 3 years and ₹ 2,660 in 5 years on simple interest. The value of sum is:

2023: 28 May Shift 1

If Rs 64 amounts to Rs 83.20 in 2 years on simple interest, then how much will Rs 86 amount to in 4 years at the same rate percent per annum ?

2026: 24 May Shift 1

At what rate of compound interest per annum, a sum of Rs 1800 becomes Rs 2178 in two years?

If a certain sum becomes three times in 4 years at compound interest, then in how many years, will it become 9 times?

Solution

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