Mathematics · Financial Mathematics
A high-net-worth individual is considering a retirement plan that involves depositing a lump sum into a guaranteed interest account today. The account offers an interest rate of 7% per annum for the first five years, after which the rate is expected to increase to 8% per annum for the subsequent ten years. The individual wants to know how much they should deposit today to ensure they can withdraw ₹1,00,000 at the end of every year for fifteen years, starting one year from today. Which of the following best describes the correct approach to this multi-stage valuation problem?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Simply average the interest rates (7.5%) and use the standard annuity formula for fifteen years to find the initial deposit amount.
- 2Calculate the present value of the first five payments at 7% and add it to the present value of the remaining ten payments, making sure to discount the second group twice: once to the end of year five at 8% and once to today at 7%.✓
- 3Use the 8% rate for all fifteen years as it is the higher rate and provides a more conservative estimate for the required initial investment.
- 4Calculate the future value of the withdrawals at 7% and then divide by the total number of years to determine today's deposit.
Correct answer
Calculate the present value of the first five payments at 7% and add it to the present value of the remaining ten payments, making sure to discount the second group twice: once to the end of year five at 8% and once to today at 7%.
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