Question

Your father, who is 60, plans to retire in 2 years, and he expects to live independently for 3 years. he wants a retirement income that has, in the first year, the same purchasing power as $40,000 has today. however, his retirement income will be a fixed amount, so his real income will decline over time. his retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments. inflation is expected to be constant at 5%. your father has $100,000 in savings now, and he can earn 8% on savings now and in the future. how much must he save each year, starting today, to meet his retirement goals?

Answer 1

To determine the annual savings needed for the father's retirement income, we calculate the present value of the desired income adjusted for inflation, and then find the annual contributions required using the future value of an annuity formula considering an 8% savings rate.

Step-by-step explanation:

To solve this problem, we need to account for both inflation and the interest rate. First, we calculate the real retirement income needed each year considering a 5% inflation rate. The present value of the first retirement payment two years from now would be equal to $40,000/(1+0.05)^2. Similarly, the second and third payments will be discounted more due to inflation. The present value of all three payments must be equal to the sum of his savings plus the present value of his annual contributions compounded at an 8% interest rate.

The present value of the retirement payments is calculated as follows:

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• First year's payment: $40,000 / (1 + 0.05)^2
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• Second year's payment: $40,000 / (1 + 0.05)^3
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• Third year's payment: $40,000 / (1 + 0.05)^4

Now we sum the present values of these payments to determine the total amount required at retirement. Once we have this total, we can use the formula for the future value of an annuity to solve for the annual savings amount he needs to contribute.

Let's denote the amount to be saved each year as X. Given the 8% earning rate, he will make two deposits, one today and one a year from today. The future value of these savings two years from now can be calculated using the formula: X + X(1 + 0.08). This future value, plus his current savings of $100,000 compounded once at 8%, must equal the previously calculated total present value of the retirement payments.

This results in an equation that can be solved for X, the annual savings needed.

This involves the concept of time value of money and adjusting for inflation to maintain purchasing power in retirement.