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How much must you save annually, beginning 1 year from now, in order to accumulate $2,500,000...

How much must you save annually, beginning 1 year from now, in order to accumulate $2,500,000 by the end of 35 years to cover your living expenses in retirement? Assume the funds in your IRA earn 10% annually. Also, how much total interest has been earned on your savings? Note: This problem is the future value of an ordinary annuity (FVAord) and I am asking you to find the annual PMT (or C as our authors note in the text). Finally, please round your answer to the nearest whole dollar ($1).

Annual Payments (PMT, of C)=

Total Interest Earned =

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Homework Answers

Answer #1

Future Value (F.V.) required = $2,500,000

Time period (n) = 35 years

Interest rate (r) = 10%

Let the Annual Annuity be to be beginning year 1 from now be "PMT"

Step 1 : Calculation of Annuity

Formula for Future Value of Annuity

2500000 = PMT ((1+0.10)35 -1) / 0.10

2500000 = PMT (28.1024368 -1) / 0.10

2500000 = PMT* 27.1024368 / 0.10

2500000 = PMT* 271.024368

PMT = $9224.26

Annual Payments (PMT or C) = $9,224.26

Step 2 : Calculation of Interest earned

Total amount of Principal invested for 35 years = Annuity *35 years = $9224.26 *35 = $322,849.20

Total Interest earned = Future value - Total Principal Invested

= $2,500,000 - 322,849.20

= $2,177,150.80

Total Interest Earned = $2,177,150.80

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