Question

Calculate the effective annual rate of compound interest equivalent to nominal rate of 18% per annum compounded half yearly and at that effective annual rate what will be the amount received if Rs. 10,000 is invested for half year?
1. 18.81%, Rs. 11881
2. 16.81%, Rs. 10881
3. 18.81%, Rs. 10881
4. 16.81%, Rs. 11881

Answer 1

Correct Answer - Option 1 : 18.81%, Rs. 11881

Given:

R = 18% p.a.

P = Rs. 10000

N = 1 / 2 year

Formula used:

Effective rate = R + R + (R² / 100)

A = P × {1 + (R / 100)}^N

Where P = Principal amount, R = Rate of interest in %, N = Number of years

Calculation:

Here, Rate of interest compounded half yearly = (18/2)%

⇒ Effective annual rate = 9 + 9 + (81/100)

⇒ Effective annual rate = 18.81%

A = 10,000 × {1 + (18.81 / 100)}

⇒ A = 10,000 + 1881

⇒ A = 11881

∴ Required answer is 18.81% and Rs. 11,881