Multiple choice

Raj deposited a specific sum in a bank at an annual compound interest rate. If the interest earned at the end of the third and fifth years amounts to Rs. 700 and Rs. 1,450.50, respectively, calculate the interest accrued by him if the amount is deposited for the eleven years, expressed in INR.

  1. 2,905.56

  2. 6,925.65

  3. 12,905.56

  4. 19,205.65

  5. 30,105.65
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and r be the annual interest rate. Interest at end of year n is P(1+r)^(n-1)*r. Ratio of interest at year 5 to year 3 is (1+r)^2 = 1450.50 / 700 = 2.07214. Thus 1+r = sqrt(2.07214) = 1.44. The interest at year 11 is 700 * (1.44)^8 = 700 * 18.4365 = 12905.56.

AI explanation

The interest accrued at the end of a specific year in compound interest is simply the interest on the accumulated amount from the previous year, meaning the interest values form a geometric progression. The ratio of the interest from the fifth year to the interest from the third year is 1450.50 divided by 700, which equals 2.07214, and taking the square root gives the annual multiplier of 1.43935. The interest for the eleventh year is found by multiplying the third year interest by this ratio raised to the power of 8, resulting in 12905.56 INR.

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