Arun took a loan of Rs. 390625 from Kuber Finance. If the company char

1.	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?
Answer» 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.

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?

Answer»

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.