Find the difference between the simple interest and the compound interest on Rs. 5000 for 2 years at 9% per annum.
Present value = Rs.5000
Interest rate = 9% per annum
Time = 2 years
Simple interest (SI) = PRT/100 [where, P = Present value
R = Interest rate, T = Time]
∴ SI = (5000 × 9 × 2)/100
⇒ SI = 50 × 9 × 2
⇒ SI = 900
Now,
Compound interest (CI),
Amount (A) = P (1 + R/100)n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 5000 (1 + 9/100)2
⇒ A = 5000 (109/100)2
⇒ A = 5000 (1.09)2
⇒ A = 5000 × 1.1881
⇒ A = 5940.5
∴ Amount = Rs.5940.5
∴ Compound interest = Rs.(5940.5 – 5000)
= Rs.940.5
Now,
Difference between the simple interest and the compound interest = (CI – SI)
= (940.5 – 900)
= 40.5