Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Tk. 4000 for 2 years at 10% per annum. The sum placed on simple interest is-

Question: Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Tk. 4000 for 2 years at 10% per annum. The sum placed on simple interest is

Solution:
Given,
principal P = Tk. 4000
Compound rate, r = 10% per annum
Time n = 2 years

Amount,
C = P(1 + r)ⁿ
= 4,000(1 + 10/100)²
= 4,000(11/10)²
= (4,000 × 121)/100
= 4840
∴ Compound interest =Tk. (4840 - 4000)
= Tk. 840

∴ Simple interest I = (840 ÷ 2) = Tk. 420
Rate r = 8%
Time n = 3 years

We know,
P = I/rn
= 420/{(8/100) × 3}
= (420 × 100)/(8 × 3)
= 1750