Your parents are giving you $180 a month for 4 years while you are in college. At an interest rate of .43 percent per month, what are these payments worth to you when you first start college?

Multiple Choice

$9,573.53

$7,791.59

$7,645.09

$7,531.87

$7,402.01

This is a present value (PV) problem involving an annuity. We are tasked with finding the present value of monthly payments of $180 over 4 years, with an interest rate of 0.43% per month.

The formula to calculate the present value of an annuity is:

\[
PV = P \times \frac{1 - (1 + r)^{-n}}{r}
\]

Where:
- $P$ is the payment amount ($180),
- $r$ is the monthly interest rate (0.43% = 0.0043),
- $n$ is the total number of payments (4 years × 12 months = 48 payments).

Let me calculate this value.The present value of the payments when you first start college is approximately **$7,791.59**.

### Answer: $7,791.59

Would you like any further details or have questions on the calculation? Here are 5 related questions to consider:

1. How does changing the interest rate affect the present value of the annuity?
2. What would the future value of these payments be if left to grow at the same interest rate?
3. How would the present value change if the payments were made bi-weekly instead of monthly?
4. What if the payments were to last for 5 years instead of 4?
5. How would a one-time lump-sum payment compare to these regular monthly payments in present value?

### Tip: The higher the interest rate, the lower the present value of future payments.

Your parents are giving you $180 a month for 4 years while you are in college. At an interest rate of .43 percent per month, what are these payments worth to you when you first start college?

Calculate the present value of receiving $180 per month for 4 years, given an interest rate of 0.43% per month. This problem involves concepts such as annuities, present value calculations, and the effect of interest rates on future payments. Perfect for college-level finance and economics students.

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