SOLUTION: Please help me, I have been trying to solve this for 2 days. Jerry has just received an inheritance of $50,000, and he would like to use it to help him with his retirement. Si

Question 178315This question is from textbook Math its Power and Utility
: Please help me, I have been trying to solve this for 2 days.
Jerry has just received an inheritance of $50,000, and he would like to use it to help him with his retirement. Since Jerry is 25 years old, he figures that the $50,000 can be invested for 40 years before he will need to use it for retirement. Jerry wants to know what interest rate would be necessary for the $50,000 to grow to provide an amount so that he can have a monthly income of $4,000 earned from the interest only. Assume that Jerry is able to invest in real estate and can earn a 12% return on his investment.

I=Prt; first I found out the amount Jerry would have after 40 years at 12% interest.
I=50000.00(.12)(40)
I=240,000.00
Then I took the 240,000.00 and used the same formula: I=Prt
4000.00=240,000.00(r)(1/12)
12*4000.=240,000.00(r)(1/12)*12
48000.00=240,000.00r (divide both sides by 240,000.00
I=.20 or 20%
I am doing this class online and so when I input the answer it tells me if the answer is correct or not. I don't understand what I am doing wrong. PLEASE HELP ME I AM DESPERATE AT THIS POINT!!!! Thank you so much in advance!!

This question is from textbook Math its Power and Utility

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Jerry has just received an inheritance of $50,000, and he would like to use it to help him with his retirement. Since Jerry is 25 years old, he figures that the $50,000 can be invested for 40 years before he will need to use it for retirement. Jerry wants to know what interest rate would be necessary for the $50,000 to grow to provide an amount so that he can have a monthly income of $4,000 earned from the interest only. Assume that Jerry is able to invest in real estate and can earn a 12% return on his investment.
:
I.m not sure what you are doing here, see if this makes sense to you
:
First find out how much required to produce $4000 a month interest at 12%
:
12% per yr is 1% per month so we have
p*r*t = 4000
t = 1
r = .01
find p
p * .01 * 1 =
.01p = 4000
p =
p = $400,000 will be the required amt
;
Now we want to find out what interest rate will produce $400,000 in 40 yrs
with $50,000 initial investment. Assume it's compounded annually
Ao(1+r)^t = A
where
A = final amt (400000)
Ao = initial amt (50000)
t = time (40 yrs)
r = interest rate (decimal)
:
50000(1+r)^40 = 400000
(1+r)^40 =
(1+r)^40 = 8
40*log(1+r) = log(8); log equiv of exponents
40*log(1+r) = .90309
log(1+r) =
log(1+r) = .022577
Find the 10^x of each side
1 + r = 1.05336
r = 1.05336 - 1
r = .05336 ~ 5.3% interest will produce $400,000 after 40 yrs compounded annually
:
Sorry I got i mixed up with r, hope it didn't confuse you. Carl
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