Question

Asha invests ₹ 8000 at a certain rate for 3 years compounded annually. She finds that at the end of one year it amounts to ₹ 9200. Calculate

1. the rate of interest 
2. the interest accrued in the second year 
3. the amount at the end of third year.

Answer 1

Based on the problem Asha faces, let’s break down the calculations:

i. Rate of interest:

Asha invests ₹ 8,000 and at the end of the first year, the amount is ₹ 9,200. This implies the interest earned for the first year is ₹ 9,200 – ₹ 8000 = ₹ 1,200.

We can calculate the rate of interest (R) using the compound interest formula for one year:

`A = P(1 + R/100)^n`

Where:

• A = 9200,
• P = 8000,
• n = 1 year.

Substituting into the formula:

`9200 = 8000(1 + R/100)`

⇒ `9200/8000 = (1 + R/100)`

⇒ `1.15 = 1 + R/100`

⇒ `R/100 = 0.15`

⇒ R = 15%

So, the rate of interest is 15%.

ii. Interest accrued in the second year:

After the first year, the principal for the second year is ₹ 9,200.

Now, we calculate the interest for the second year using the same rate of interest:

Interest for 2^nd year = `9200 xx 15/100`

Interest for 2^nd year = ₹ 1,380

So, the interest accrued in the second year is ₹ 1,380.

iii. Amount at the end of the third year:

At the end of the second year, the new principal is ₹ 9,200 + ₹ 1,380 = ₹ 10,580.

For the third year, the interest is:

Interest for 3^rd year = `10,580 xx 15/100`

Interest for 3^rd year = ₹ 1,587

Therefore, the amount at the end of the third year is A = 10,580 + 1,587 = ₹ 12,167