Question

3.

Every 6 months, Reuben Lopez puts $420 into an account paying 10% compounded semiannually.
Find the account balance after 15 years.


$29,299.53

$27,904.32

$31,500.00

$29,315.00

Answer 1

To solve this we are going to use the future value of annuity due formula:
`FV=(1+ (r)/(n) )*P[ ((1+ (r)/(n))^(kt)-1 )/( (r)/(n) ) ]`
where

`FV` is the future value

`P` is the periodic deposit

`r` is the interest rate in decimal form

`n` is the number of times the interest is compounded per year

`k` is the number of deposits per year

We know for our problem that
`P=420` and
`t=15`. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
`r= (10)/(100) =0.1`. Since Ruben makes the deposits every 6 months,
`k=2`. The interest is compounded semiannually, so 2 times per year; therefore,
`k=2`.
Lets replace the values in our formula:


`FV=(1+ (r)/(n) )*P[ ((1+ (r)/(n))^(kt)-1 )/( (r)/(n) ) ]`

`FV=(1+ (0.1)/(2) )*420[ ((1+ (0.1)/(2))^((2)(15))-1 )/( (01)/(2) ) ]`

`FV=29299.53`

We can conclude that the correct answer is $29,299.53