A sum of money is put on compound interest for 2 years at 20%. It would fetch Tk. 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Question: A sum of money is put on compound interest for 2 years at 20%. It would fetch Tk. 482 more if the interest is payable half yearly than if it were payable yearly. Find the sum.

Solution:
Let the Principal = Tk. 100
When compounded annually,
A = 100 [1 + 20/100]²
= 100 × 1.2 × 1.2
= 144

When compounded half yearly,
A = 100[1 + 10/100]⁴
= 100 × 1.1 × 1.1 × 1.1 × 1.1
= 146.41

Difference, 146.41 - 144 = 2.41

If difference is 2.41, then Principal = Tk. 100
If difference is 482, then Principal = (100/2.41) × 482 = 20000