Harpreet borrowed Rs. 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
Present value = Rs.20000
Interest rate = 12% per annum
Time = 2 years
Simple interest (SI) = PRT/100 [where, P = Present value
R = Interest rate, T = Time]
∴ SI = (20000 × 12 × 2)/100
⇒ SI = 200 × 12 × 2
⇒ SI = 4800
Now,
Amount (A) = P (1 + R/100)n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 20000 (1 + 12/100)2
⇒ A = 20000 (112/100)2
⇒ A = 20000 (1.12)2
⇒ A = 20000 × 1.2544
⇒ A = 25088
∴ Amount = Rs.25088
∴ Compound interest = Rs.(25088 – 20000)
= Rs.5088
Now,
(CI – SI) = 5088 -4800
= Rs.288
∴ The amount of money Harpreet will gain after two years = Rs.288