Question

If you put $2,000 a year for 3 years into an IRA that earns 3% a year, how much will you have saved at the end of the third year?

Answer 1

To calculate the total savings after putting $2,000 a year for 3 years into an IRA with a 3% annual interest rate, you must calculate the compounded amount for each deposit separately for the respective number of years and then sum them up. The total amount saved would be $6,367.26.

Step-by-step explanation:

When you put $2,000 a year for 3 years into an IRA that earns 3% a year, we can calculate the total amount saved at the end of the third year using the formula for compound interest. However, because the deposits are done annually, we have to do calculations for each year separately as each deposit will have a different amount of time to grow.

For the first $2,000 deposit which compounds for 3 years, the calculation is as follows:
First Deposit = $2,000 * (1 + 0.03)^3

For the second $2,000 deposit which compounds for 2 years, the calculation goes:
Second Deposit = $2,000 * (1 + 0.03)^2

And the third $2,000 deposit which compounds for 1 year will be:
Third Deposit = $2,000 * (1 + 0.03)^1

After calculating the compounded amount for each deposit, you add them up to get the total amount saved in the IRA after 3 years:

1. First Deposit after 3 years = $2,185.46
2. Second Deposit after 2 years = $2,121.80
3. Third Deposit after 1 year = $2,060.00

Adding these amounts, the total savings at the end of the third year would be:

Total = First Deposit + Second Deposit + Third Deposit = $6,367.26