Bowen invested an average of $350 per month since age 44 in various securities for his retirement savings. His investments averaged a 5% annual rate of return until he retired at age 69. Given the same monthly investment and rate of return, how much more would Bowen have in his retirement savings had he started investing at age 30? Assume monthly compounding.

Question

anonymous · Answer

@SkiTTleoooo47 @nicf @LissaBaby989 @AlternationRevolver97 @mathmate @math&ing001 @morningskye123

mathmate · Answer

Do you know the compound interest formula?
It should be a straight computation with the given data.

anonymous · Answer

yeah its FV   =   P (1  +  r / n)Yn

mathmate · Answer

Here we have 
t=69-30=39 years
n=12 times compounding a year
i=annual interest rate
R=(1+i/n)=monthly compounding rate
A=amount accumulated at the end of t years
M=monthly amount/payment
$$ A=M+MR+MR^2 +MR^3+...+MR^{nt-1}$$
$$=\frac{MR^{nt}}{R-1}$$
$$=\frac{350(1+0.065/12)^{12*39}}{0.065/12}$$
= a little less than $810,000

anonymous · Answer

$379,353.51

$61,740.00

$295,594.30

$132,300.00 
these are the answer choices im confused :/.

mathmate · Answer

The question requires the difference between returns by starting at different ages.  So you can use the same formula and calculate the two returns.  Take the difference, and it will match one of the given answers.
Note that the example I gave used an annual interest rate of 0.065 and not 0.05.

anonymous · Answer

ok thanks

mathmate · Answer

You're welcome! :)

goformit100 · Answer

Hello, and A Warm Welcome to Open Study!