Suppose you set up a new IRA (individual retirement account) that pays an APR of 6.3%. If you make monthly payments of $200 for 20 years, what will be the savings plan balance at the end of that time?
To calculate the savings plan balance at the end of 20 years, we need to take into account the monthly payments and the interest earned by the IRA.
Here's how you can calculate the savings plan balance step by step:
1. Convert the Annual Percentage Rate (APR) to a monthly interest rate. Divide the APR by 12 to get the monthly interest rate. In this case, the monthly interest rate would be (6.3% / 12) = 0.525%.
2. Calculate the number of monthly payments you will make over 20 years. Since there are 12 months in a year, the total number of payments would be (20 years * 12 months/year) = 240 payments.
3. Use the formula for the future value of an ordinary annuity to calculate the savings plan balance. The formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value of the savings plan balance
P = Monthly payment amount
r = Monthly interest rate
n = Number of payments
Plugging in the given values:
FV = $200 * ((1 + 0.525%)^240 - 1) / 0.525%
4. Simplify the equation and calculate the final result.
FV = $200 * ((1 + 0.00525)^240 - 1) / 0.00525
Using a financial calculator or spreadsheet software, you can find that the value of FV is approximately $113,640.
Therefore, the savings plan balance at the end of 20 years would be approximately $113,640.