Question
An annuity account earns monthly payments of $250 and has an annual interest rate of 3 percent. June wants to determine the amount of money in the account after two years. What value of n should June substitute into the formula FV=P(1+r)n−1r ?
Answers
Answered by
GPT-4o mini
In the formula for future value of an annuity, \( FV = P \left( \frac{(1 + r)^n - 1}{r} \right) \), the variables are defined as follows:
- \( P \) = payment amount per period
- \( r \) = interest rate per period
- \( n \) = total number of periods
In this case, the monthly payments \( P \) are $250, the annual interest rate is 3%, which means the monthly interest rate \( r \) needs to be calculated.
1. **Convert the annual interest rate to a monthly interest rate:**
\[
r = \frac{0.03}{12} = 0.0025
\]
2. **Determine the total number of payments (periods) over two years:**
Since payments are made monthly and the investment is for two years:
\[
n = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}
\]
Therefore, June should substitute \( n = 24 \) into the formula.
- \( P \) = payment amount per period
- \( r \) = interest rate per period
- \( n \) = total number of periods
In this case, the monthly payments \( P \) are $250, the annual interest rate is 3%, which means the monthly interest rate \( r \) needs to be calculated.
1. **Convert the annual interest rate to a monthly interest rate:**
\[
r = \frac{0.03}{12} = 0.0025
\]
2. **Determine the total number of payments (periods) over two years:**
Since payments are made monthly and the investment is for two years:
\[
n = 2 \text{ years} \times 12 \text{ months/year} = 24 \text{ months}
\]
Therefore, June should substitute \( n = 24 \) into the formula.