A certain sum was invested for three years in a scheme in which the interest gets compounded annuall...........

Quantitative Aptitude (MTS) Compound Interest

A certain sum was invested for three years in a scheme in which the interest gets compounded annually. During the first two

years,the scheme provided growths at the rates of 80% and 60%,respectively,but during the third year there was a decline by

40%. What was the overall interest rate for three years?

This questions was previously asked in

SSC MTS 12th October 2021 Shift-2

24%

20%

22.5%

48.6%

- The investment grows by 80% in the first year. This means the value becomes 1.8 times the original amount.

- In the second year, it grows by 60%. So, the new value is 1.6 times its value at the end of the first year.

- In the third year, there is a decline of 40%. Therefore, the value becomes 0.6 times its value at the end of the second year.

- We calculate the overall growth rate by multiplying these factors: \(1.8 \times 1.6 \times 0.6\).

- This equals 1.728, which is equivalent to a 72.8% overall growth over three years.

- The annual growth rate can be found using \((1 + r)^3 = 1.728\). Solving gives approximately \(r \approx 0.20\).

- This equates to a 20% annual interest rate.

Option 2: 20% is the correct answer.

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