Question

You put $300 at the end of each month in an investment plan that pays an APR of 7%. How much will you have after 18 years? Compare this amount to the total deposits made over the time period.
a.
$129,201.10; $64,800
c.
$129,216.31; $64,800
b.
$129,211.25; $64,775
d.
$129,218.51; $64,775

Answer 1

This is a future value of annuity problem

http://www.investopedia.com/terms/f/future-value-annuity.asp


\[\Large FV = C*\left[\frac{(1+i)^n-1}{i}\right]\]


FV = future value after n periods
C = cashflow (aka amount of money deposited each time)
i = interest rate per period
n = number of periods


In this case,


FV = unknown
C = 300
i = 7%/12 = 0.07/12 = 0.00583333333333
n = 18*12 = 216


Now plug this into the formula given on the link. Then use a calculator to compute



\[\Large FV = C*\left[\frac{(1+i)^n-1}{i}\right]\]


\[\Large FV = 300*\left[\frac{(1+0.00583333333333)^{216}-1}{0.00583333333333}\right]\]


\[\Large FV \approx 129,216.307980597\]


\[\Large FV \approx 129,216.31\]


Don't forget to round to the nearest penny

Answer 2

So after 18 years, you'll have $129,216.31 in the account


This is assuming you deposit $300 each month (every month for 18 years).


Compare this with just storing $300 under your mattress and you would have 300*12*18 = $64,800

Answer 3

So clearly depositing the $300 into a bank account is the better choice. You practically double your money.