Owen plans to deposit $4,000 in a traditional IRA at the end of every six months for the next 10 years.

Question

 

Find the future value if funds earn 10% compounded semiannually.

$35,345.01
$33,065.95
$132,263.80
$138,877.00

$35,345.01$33,065.95$132,263.80$138,877.00

Answer 1

To calculate the future value of Owen’s deposits with semiannual compounding, we’ll use the future value of an ordinary annuity formula:

where:

• = amount of each deposit ($4,000),

• = interest rate per compounding period,

• = total number of deposits.

Step-by-Step Calculation

1. Convert the annual interest rate to the rate per period:

• The annual rate is 10%, or 0.10.

• Since interest compounds semiannually, divide by 2:

2. Calculate the total number of deposits:

• Deposits are made twice a year for 10 years, so:

3. Plug into the formula:

4. Solve the equation:

• First, calculate :

• Then, subtract 1:

• Finally, divide by 0.05 and multiply by $4,000:

Answer

The future value of Owen’s deposits, if they earn 10% compounded semiannually, is $132,263.80.