Michael borrowed Rs.16000 from a finance company at 10% per annum, com

1.	Michael borrowed Rs.16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1 (1/2) years?
Answer» Present value = Rs.16000 Interest rate = 10% per annum Time = (3/2) years ∵ Interest is compounded half-yearly. ∴ Amount (A) = P [1 + (R/2)/100]²ⁿ [Where, P = Present value R = Annual interest rate n = Time in years] ∴ A = 16000 [1 + (10/2)/100]³ ⇒ A = 16000 [1 + 5/100]³ ⇒ A = 16000 [1 + 1/20]³ ⇒ A = 16000 [21/20]³ ⇒ A = 16000 × 21/20 × 21/20 × 21/20 ⇒ A = 2 × 21 × 21 × 21 ⇒ A = 18522 ∴ Amount = Rs.18522

Michael borrowed Rs.16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after 1 (1/2) years?

Answer»

Present value = Rs.16000

Interest rate = 10% per annum

Time = (3/2) years

∵ Interest is compounded half-yearly.

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

R = Annual interest rate

n = Time in years]

∴ A = 16000 [1 + (10/2)/100]³

⇒ A = 16000 [1 + 5/100]³

⇒ A = 16000 [1 + 1/20]³

⇒ A = 16000 [21/20]³

⇒ A = 16000 × 21/20 × 21/20 × 21/20

⇒ A = 2 × 21 × 21 × 21

⇒ A = 18522

∴ Amount = Rs.18522