Brenton invested an average of $250 per month since age 39 in various securities for his retirement savings. His investments averaged a 6% annual rate of return until he retired at age 66. Given the same monthly investment and rate of return, how much more would Brenton have in his retirement savings had he started investing at age 25? Assume monthly compounding.

Question

rockinhood · Answer

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retireed · Answer

Use your equation given to you in your book or notes and calculate the amounts for both starting ages and subtract the larger one for the smaller one

dumbcow · Answer

sorry i misread the question, you need formula for sum of geometric series
$$\rightarrow 250 (1 + (1+r) + (1+r)^2 + ...(1+r)^n)$$
$$S(n) =250 \frac{(1+r)^n - 1}{r}$$
r = monthly rate = 6% /12 = .5%
n = num of months for each case

rockinhood · Answer

So how do I solve an equation of that size ??

dumbcow · Answer

you dont have to, you are given all the variables.... just put it into calculator

dumbcow · Answer

For 1st case. 66-39 = 27 yrs = 27*12 = 324 months ..... plug in n = 324

2nd case. 66-25 = 41 yrs = 41*12 = 492 months ...... plug in n = 492

rockinhood · Answer

I don't think I'm plugging it in right ?

mathmate · Answer

@rockinhood 
what did you get plugging the numbers in, 
1. for 27 years,
2. for 41 years
and
3. the difference?

rockinhood · Answer

decimals.
1. 5.66
2. 2.17
3. 3.49

rockinhood · Answer

@mathmate

hero · Answer

@dumbcow gave you more than enough to finish solving on your own imo.

hero · Answer

On a side note, you should invest in a good calculator--preferably ti-nspire.

rockinhood · Answer

Oops, found my problem.  I was doing .5 instead of .005

rockinhood · Answer

Thanks for the.. encouragement  ?? I guess

rockinhood · Answer

Yeah ended up with 

   5316.64
- 2016.37
_______________
   3,330.27

mathmate · Answer

From formula above:
$FV(P,i,n) =P \frac{(1+r)^n - 1}{r}$
FV=future value
r=interest per month (in fractions, 0.06/12 for 6% per annum)
n=number of months, (number of years * 12)
If you are using a calculator, remember that all numbers in the numerator must be enclosed in parentheses.

So please try the calculations again.
Hint: the FV for 27 and 41 years both are in the hundreds of thousand dollars.

mathmate · Answer

You're close, but probably did something wrong with the $250 monthly payment.
Please check the calculations.