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A 52-year-old client asks an accountant

A 52-year-old client asks an accountant how to plan for his future retirement at age 62. He expects income from Social Security in the amount of $21,600 per year and a retirement pension of $40,500 per year from his employer. He wants to make monthly contributions to an investment plan that pays 8%, compounded monthly, for 10 years so that he will have a total income of $83,700 per year for 30 years. What will the size of the monthly contributions have to be to accomplish this goal, if it is assumed that money will be worth 8%, compounded continuously, throughout the period after he is 62?

To help you answer this question, complete the following.

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1. How much money must the client withdraw annually from his investment plan during his retirement so that his total income goal is met?

2. How much money S must the client’s account contain when he is 62 so that it will generate this annual amount for 30 years? (Him: S can be considered the present value over 30 years of a continuous income stream with the amount you found in Question 1 as its annual rate of flow.)

3. The monthly contribution R that would, after 10 years, amount to the present value S found in Question 2 can be obtained from the formula:


where i represents the monthly interest rate and n the number of months. Find the client’s monthly contribution, R.

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