Billy Bob, who is 22, won a prize of $5000 at McDonalds. He invests the money at 8% compounded quarterly for 43 years until he retires. When he retires, he then reinvests the money at 7% compounded monthly and makes equal monthly withdrawals for a further 25 years at which time the money would run out. How much money would he get each month? Show all work. Round final answers appropriately.
My final answer is $10,551.10 and I wanted to make sure that was correct. Thank you!
The first thing to do is to find the Future Value of the Billy Bob's $5,000 investment @ 8% for 43 years.
FV = 5,000 x [1 + 0.08/4]^(43*4)
FV = 5,000 x 1.02^172
FV = 5,000 x 30.14598946562.....
FV =$150,729.95 - This is what the retirement fund of Billy Bob is worth at 65.
The next thing to do is to calculate the monthly payments that he will receive for the next 25 years.
PV=P{[1 + R]^N - 1 / [1 + R]^N} / R
150,729.95 = P x {[1 + 0.07/12]^(25*12) - 1 / [1 + 0.07/12]^(25*12)} / 0.07/12
150,729.95 = P x 141.48690338........
PAYMENT = 150,729.95 / 141.48690338 =$1,065.33 - This is the monthly payment that Billy Bob should receive each and every month for 25 years.
P.S. If you have any questions, just let us know here.
I have this sme question. The monthly payment isn’t the right amount. The first part seems to be right.
Hello: ALL the calculations are accurate to the cent based on the information you have given. Your monthly payment of $10,551.10 is way, way out!! You would have to start your annuity with a balance of over $1,500,000 !!!. If the retirement payments start at the BEGINNING of the month, then the payments will be $1,059.15 each and every month. Check your numbers carefully.
I know 10,551.10 is wrong. it was typed wrong it was suposed to be $1,551.10. your answer $1,065.33 is wrong too. After I give three wrong answers the correct answer is given. It says $1,044.74 per month. It's not much different than what you said, but it still a wrong answer. Maybe it's a different formula than the one you used.
OK, I know now what the problem is. Look at your question where you say "7% compounded monthly".
Your 7% is NOT compounded monthly!!!. It is compounded ANNUALLY!!. Which means we have to convert the interest rate of 7% compounded annually to compounded monthly.
And this is how you do that: 1.07^(1/12) =1.00565414538 - 1 x 1,200 =6.784974465%. This is the interest compounded monthly!!. Which is equivalent to 7% compounded annually. This will give you a monthly payment of $1,044.74 when you enter it in the above formula that I used.
