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An amount of 12000 was borrowed partly at 4% simple interest and partly at 6% compound interest. Find out the time period when interest obtained through simple interest equates to that of interest obtained through compound interest after 4 years. Assume that amount borrowed is in ratio 5 : 7

An amount of 12000 was borrowed partly at 4% simple interest and partly at 6% compound interest. Find out the time period when interest obtained through simple interest equates to that of interest obtained through compound interest after 4 years. Assume that amount borrowed is in ratio 5 : 7 Correct Answer 9.17

⇒ Amount borrowed is in ratio 5 : 7

hence,

principal amount for simple interest = 5 / 12 × 12000 = 5000

And amount borrowed at compound interest = 7000 (∵ 12000 – 5000 = 7000)

⇒ Simple interest = A = p (1 + rt) –––– (Rate: 4%)

⇒ Compound interest A = p (1 + (r / n)) nt (Rate: 6%) (here, t = 1)

Amount through compound interest = 7000 (1 + 0.06)4

⇒ 7000 (1.06)4 = 7000 × 1.262

⇒ Amount = 8, 834

Now,

⇒ interest earned = 8834 – 7000 = 1834

I = PRT / 100

Hence,

1834 = 5000 × 4 × t / 100

⇒ 1834 / 200 = t

⇒ t = 9.17 Years

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