Arithmetic

Simple & Compound Interest

Medium

A certain amount, when put at a compound rate of interest, becomes double in 5 years. In how many years will the amount become eight times?

10 years

12 years

25 years

15 years

✅ Correct Option: 4

When an amount is placed at compound interest and becomes double in 5 years, the time required for it to become eight times can be found using the doubling pattern.

In compound interest, the amount grows by multiplication. Since the amount doubles in 5 years:

After 5 years: Amount $= 2 \times$ original

After 10 years: Amount $= 2 \times 2 = 4 \times$ original

After 15 years: Amount $= 4 \times 2 = 8 \times$ original

Using the compound interest formula $A = P(1 + r)^t$

Since the amount doubles in 5 years:

$2 = (1 + r)^5$

For the amount to become 8 times:

$8 = (1 + r)^t$

Since $8 = 2^3$ :

$8 = 2^3$

$8 = [(1 + r)^5]^3$

$8 = (1 + r)^{15}$

Therefore $t = 15$ years

The amount will become eight times in 15 years.

When money doubles in $n$ years, it becomes $2^k$ times in $k \times n$ years. Here, $8 = 2^3$ and $n = 5$ , so the time required is $3 \times 5 = 15$ years.

2025: 14 May Shift 1

A sum of money becomes thrice of itself in 20 years. Find the simple interest rate per annum?

2025: 29 May Shift 1

What is the rate of simple interest for the last 5 years if the sum of ₹ 480 becomes ₹ 792 in 11 years and the rate of interest for the first 6 years is 5%?

2025: 13 May Shift 2

Mr. X invested one fourth of his capital at 8%, one third at 7% and the remaining part at 10%. If his annual simple interest on this investment is Rs 510, then the total capital invested by Mr. X is?

2026: 19 May Shift 2

A man invested $\frac{1}{3}$ of his capital at 8%, $\frac{1}{4}$ at 10% and the remainder at 12%. If his annual income is ₹671, find the capital.

2026: 12 May Shift 2

Consider the simple interest of the following:

(A) A sum of Rs 1200 at 3% per annum for 3 years.

(B) A sum of Rs 5500 at 7% per annum for 2 years.

(D) A sum of Rs 2000 at 14% per annum for 4 years.

Arrange the above in descending order.

Choose the correct answer from the options given below:

2025: 23 May Shift 1

The simple interest on a sum of Rs 1550 for 2 yrs is Rs 20 more than the simple interest on Rs 1450 for the same duration (the rate of interest is the same in both the cases). Find the rate of interest.

A certain amount, when put at a compound rate of interest, becomes double in 5 years. In how many years will the amount become eight times?

Solution

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