Compound interest rate of 6% p.a. is given for the investment of Rs. 42,000 for 10 years. What is the amount at the end of the term if interest is added half-yearly?
- Rs. 54,687.3
- Rs. 63,279.4
- Rs. 75,856.7
- None of these
Explanation
Given:
- Principal (P) = Rs. 42,000
- Annual interest rate (r) = 6% = 0.06
- Time (t) = 10 years
- Interest compounded half-yearly (n = 2 times per year)
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Formula for compound interest:
Amount, A = P * (1 + r/n)^(n*t)
Substitute the values:
A = 42,000 * (1 + 0.06/2)^(2 * 10)
= 42,000 * (1 + 0.03)^20
= 42,000 * (1.03)^20
---
Calculate (1.03)^20:
(1.03)^20 ≈ 1.8061
---
So,
A ≈ 42,000 * 1.8061 ≈ Rs. 75,856.2
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