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Two stock options are available for buying. Each offers a variable rate of return of profit over a period of 10 years. For first 4 years one has an incremental rate of return which increases by 2% per year starting from 3% of the investment and stays constant at 8% for the rest of the period. The second one has a constant annual rate of return throughout and give 10% more return after 10 years. What is the annual rate of return on second option?

Two stock options are available for buying. Each offers a variable rate of return of profit over a period of 10 years. For first 4 years one has an incremental rate of return which increases by 2% per year starting from 3% of the investment and stays constant at 8% for the rest of the period. The second one has a constant annual rate of return throughout and give 10% more return after 10 years. What is the annual rate of return on second option? Correct Answer 7.92

Let the principle be X

Return in first year = 3% of X = 0.03X

Return in second year = 5% of X = 0.05X

Return in third year = 7% of X = 0.07X

Return in fourth year = 9% of X = 0.09X

For remaining 6 years = 0.08X each year = 0.08 × 6 = 0.48X

Total return = (0.48 + 0.09 + 0.07 + 0.05 + 0.03)X = 0.72X

Second option gives return 10% than first option

Let return on second option be Y

(Y - 0.72X)/0.72X = 0.1

Y = 0.72X + 0.072X = 0.792X

This is interest rate on second option at constant rate for 10 years

If rate is R then = R × 10 × X = 0.792X

R = 0.0792 = 7.9 %

∴ The annual rate of return on second option = 7.9%

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