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!

Guest Apr 20, 2017

#1**0 **

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.

Guest Apr 20, 2017

#2**0 **

I have this sme question. The monthly payment isnâ€™t the right amount. The first part seems to be right.

Guest Apr 20, 2017

#3**0 **

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.

Guest Apr 20, 2017

#4**0 **

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.

Guest Apr 20, 2017

#5**0 **

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.

Guest Apr 20, 2017