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A man borrowed Rs. 80000 from a bank at compound interest compounded half-yearly. After 2 years, the bank asked him to pay Rs. 90040 to clear his debt. What is his rate of interest?

A man borrowed Rs. 80000 from a bank at compound interest compounded half-yearly. After 2 years, the bank asked him to pay Rs. 90040 to clear his debt. What is his rate of interest? Correct Answer 6%

On a sum of Rs. P, when the compound interest at R% per annum is compounded half-yearly, the amount after n years is computed as,

Amount = P2n

Let the rate of interest be ‘R’%

⇒ 90040 = 800002 × 2

⇒ 1.1255 = 4

⇒ 1.1255 × (200)4 = (200 + R)4

⇒ 1.1255 × 16 × 108 = (200 + R)4

⇒ 18.008 × 108 = (200 + R)4

⇒ 200 + R = 2.06 × 102

⇒ R = 206 – 200 = 6%

∴ The rate of interest is 6% per annum

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