Arun took a loan of Rs. 390625 from Kuber Finance. If the company charges interest at 16% per annum, compounded quarterly, what amount will discharge his debt after one year?
Present value, P = Rs.390625
Interest rate, R = 16% per annum
Time, n = 1 year
∵ Compounded quarterly,
∴ Amount (A) = P [1 + (R/4)/100]4n [Where, P = Present value
R = Annual interest rate
n = Time in years]
∴ A = 390625 [1 + (16/4)/100]4
⇒ A = 390625 [1 + 4/100]4
⇒ A = 390625 [1 + 1/25]4
⇒ A = 390625 [26/25]4
⇒ A = 390625 × 26/25 × 26/25 × 26/25 × 26/25
⇒ A = 390625 × 456976/390625
⇒ A = 1 × 456976
⇒ A = 456976
∴ Amount = Rs.456976
∴ Arun has to pay Rs.45976 after 1 year.