Question

Find the amount and compound interest of ₹ 64000 at 5% per annum for `1 1/2` years, interest being compounded half-yearly.

Answer 1

Given:

• Principal (P) = ₹ 64000
• Rate of interest (R) = 5% per annum
• Time (T) = `1 1/2` years = 1.5 years
• Interest is compounded half-yearly

Step-wise calculation:

1. Since the interest is compounded half-yearly, number of compounding periods per year = 2.

2. Number of half-year periods, n = 1.5 years × 2 = 3 half-years.

3. Half-yearly interest rate, r = 5% ÷ 2 = 2.5%.

4. The compound amount A is calculated using the formula:

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

Plugging in the values:

`A = 64000 xx (1 + 2.5/100)^3`

A = 64000 × (1.025)³

5. Calculate (1.025)³:

(1.025)³ = 1.025 × 1.025 × 1.025

(1.025)³ = 1.076890625

6. Calculate the amount:

A = 64000 × 1.076890625

A = 68920.2

7. Compound Interest (CI) is:

CI = A – P

CI = 68920.2 – 64000

CI = 4920.2

Amount = ₹ 68920.20

Compound Interest = ₹ 4920.20

Thus, the amount after `1 1/2` years is ₹ 68920.20 and the compound interest earned is ₹ 4920.20, when interest is compounded half-yearly at 5% p.a. on ₹ 64000.