Question

7. A sum of 31,250 amounts to 35,152 in 3/2
years. Find the rate per annum, interest being compounded
semiannually.​

Answer 1

Answer :

Present value, P = Rs.31250

Interest rate, R = 8% per annum

Time, n = (3/2) years

∵ Compounded half-yearly.

∴ Amount (A) = P [1 + (R/2)/100]2n [Where, P = Present value

R = Annual interest rate

n = Time in years]

∴ A = 31250 [1 + (8/2)/100]3 [2n = 2 × 3/2]

⇒ A = 31250 [1 + 4/100]3

⇒ A = 31250 [1 + 1/25]3

⇒ A = 31250 [26/25]3

⇒ A = 31250 × 17576/15625

⇒ A = 2 × 17576

⇒ A = 35152

∴ Amount = Rs.35152

∴ Compound interest = Rs.(35152 – 31250) [∵CI = A – P]

= Rs.3902