Multiple choice

A certain sum of money, lent at a certain rate of compound interest, grows to 1.69 times of its value in 2 years. If the same sum is lent at simple interest at the same rate, in how many years/months would it double itself?

  1. 4 years

  2. 40 months

  3. 3 years

  4. 30 months

  5. 38 months
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B Correct answer
Explanation

If a sum grows to 1.69 times in 2 years at compound interest, (1+r)^2 = 1.69, so 1+r = 1.3, meaning r = 30% per annum. For simple interest, the sum doubles when the interest equals the principal, so P = P * 0.30 * t, which gives t = 1/0.30 = 3.33 years. 0.33 years is 4 months, so 3 years and 4 months equals 40 months.

AI explanation

Since the sum grows to 1.69 times in 2 years under compound interest, we have 1.69 equals 1 plus R divided by 100 all squared, meaning 1 plus R divided by 100 equals 1.3, so the rate R is 30 percent. To find the time to double the sum at simple interest, we set 2P equal to P plus P multiplied by 30 multiplied by Time divided by 100, yielding 100 divided by 30, or 10/3 years; multiplying by 12 gives the result of 40 months.

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