Question
In Example 6.2.3, Donovan started placing $75 per month into an annuity savings plan that earned 1.5% APR compounded Monthly. The future value of his account after 10 years was $9703.52. How much of the final amount was a result of earned interest? Enter your answer without a dollar sign or comma. For example, 9703.52
Answers
GPT-4o mini
To find out how much of the final amount of $9703.52 was earned from interest, we first need to calculate the total amount that Donovan contributed to the annuity savings plan over the 10 years.
1. **Calculate the total contributions:**
- Monthly contribution = $75
- Number of months in 10 years = 10 years × 12 months/year = 120 months
Total contributions = Monthly contribution × Number of months
\[
\text{Total contributions} = 75 \times 120 = 9000
\]
2. **Calculate the earned interest:**
- Future value of the account = $9703.52
- Total contributions = $9000
Earned interest = Future value - Total contributions
\[
\text{Earned interest} = 9703.52 - 9000 = 703.52
\]
Thus, the amount of the final amount that was a result of earned interest is \(703.52\).
1. **Calculate the total contributions:**
- Monthly contribution = $75
- Number of months in 10 years = 10 years × 12 months/year = 120 months
Total contributions = Monthly contribution × Number of months
\[
\text{Total contributions} = 75 \times 120 = 9000
\]
2. **Calculate the earned interest:**
- Future value of the account = $9703.52
- Total contributions = $9000
Earned interest = Future value - Total contributions
\[
\text{Earned interest} = 9703.52 - 9000 = 703.52
\]
Thus, the amount of the final amount that was a result of earned interest is \(703.52\).