Mrs. Reznik, who 27 years old, plans to retire at the age of 55. She is expectin

Question

Mrs. Reznik, who 27 years old, plans to retire at the age of 55. She is expecting a lumpsum amount (an inheritance) of $75,000 when she is 40. This lumpsum amount will be invested at 8% per year. a. Mrs. Reznik would like to be able to withdraw $120,000 per year from her retirement account for 45 years after retirement beginning a year after her retirement. How much does she need to have in her retirement account by retirement date if the interest rate is 7% per year during the post-retirement years?

b. Suppose she already has $45,000 in her retirement investment account that earns 7.5% per year. What will be the

value of this amount by her retirement date?

c. Given her goal in 2a above and the investment she already has in 2b in addition to her expected inheritance, how much does she need to invest per year (at 9% annual rate of return) beginning a year from now till retirement, in order to reach her retirement goal?

Explanation / Answer

Mrs. Reznik has 28 years till retirement

a) She wanted to withdraw 120,000 from year 55 (End of year) for 45 years

If interest rate is 7%, PV at year 55 can be calculated as follows

=PV(7%,45,-120000,0,0) = $1,632,662.59

Here 7% is the interest rate, 45 is number of years withdrawal is made, 120000 is the value of each withdraw and 0 is the future value after 45 years and 0 represents withdrawal is made at the end of the year

2. Present value is given as 45000, interest rate is given as 7.5%, number of years would be 28, so future value can be calculated in excel as follows

=FV(7.5%,28,0,-45000,0) = $340,917.67

3. Value of inheritance amount when she is 55 can be calculated as follows

PV can be taken as 75000, number of years of investment = 15, interest rate = 8%

Future value can be calculated using the formula as follows

=FV(8%,15,0,-75000,0) = $237,912.68

So she is already has $237,912.68 from her inheritance investment and $340,917.67 from investment of b

So additional funds required at retirement = $1,632,662.59 - $237,912.68 - $340,917.67 = $1,053832.24

Now this can be taken as FV, interest rate would be 9%, number of years of investment = 28, PV is 0 so PMT can be calculated as follows

=PMT(9%,28,0,-1632662.59 ,0) = $9,328.57

So investment made each year should be $9,328.57

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