Question: The Pirerras are planning to go to Europe 3 years from now and have agreed to set aside $160/month for their trip. If they deposit this money at the end of each month into a savings account paying interest at the rate of 2%/year compounded monthly, how much money will be in their travel fund at the end of the third year? (Round your answer to the nearest cent.)
1. **State the problem:**
The Pirerras deposit $160 at the end of each month into a savings account with an annual interest rate of 2% compounded monthly. We want to find the total amount in the account after 3 years.
2. **Formula used:**
We use the future value of an ordinary annuity formula:
$$FV = P \times \frac{(1 + r)^n - 1}{r}$$
where:
- $P$ is the monthly payment
- $r$ is the monthly interest rate
- $n$ is the total number of payments
3. **Identify values:**
- $P = 160$
- Annual interest rate = 2% = 0.02
- Monthly interest rate $r = \frac{0.02}{12} = 0.0016667$
- Number of months $n = 3 \times 12 = 36$
4. **Calculate the future value:**
$$FV = 160 \times \frac{(1 + 0.0016667)^{36} - 1}{0.0016667}$$
5. **Calculate $(1 + r)^n$:**
$$ (1 + 0.0016667)^{36} = 1.061678 $$
6. **Substitute and simplify:**
$$FV = 160 \times \frac{1.061678 - 1}{0.0016667} = 160 \times \frac{0.061678}{0.0016667}$$
7. **Simplify the fraction:**
$$\frac{0.061678}{0.0016667} = 37.0068$$
8. **Calculate final amount:**
$$FV = 160 \times 37.0068 = 5921.09$$
**Answer:**
The amount in the travel fund at the end of 3 years is approximately $5921.09$.