Q. 83.8( 42 Votes )

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

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

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