What single payment today would replace a payment of $1,700.00 in 1 years and a payment of $3,900.00 in 5 years if the interest rate is 3.65% compounded quarterly?

To find the single payment today that would replace the future payments of $1,700 in 1 year and $3,900 in 5 years, we need to discount these future payments to their present value using the formula for compound interest.

The formula for the present value $ PV $ of a future amount $ F $ is:

\[
PV = \frac{F}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ F $ is the future payment.
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of compounding periods per year.
- $ t $ is the number of years until the payment is made.

Given:
- Interest rate $ r = 3.65\% = 0.0365 $.
- Compounded quarterly, so $ n = 4 $.
- First payment: $ F_1 = 1,700 $, $ t_1 = 1 $.
- Second payment: $ F_2 = 3,900 $, $ t_2 = 5 $.

We will calculate the present value of both future payments and then sum them to get the total present value today.

Let's calculate this.The single payment today that would replace the future payments of $1,700 in 1 year and $3,900 in 5 years, at an interest rate of 3.65% compounded quarterly, is approximately **$4,891.45**.

Would you like further details or have any questions about this calculation?

Here are 5 related questions to expand on this topic:
1. How would the single payment change if the interest rate were compounded annually instead of quarterly?
2. What would be the total interest saved by paying the amount today instead of in the future?
3. How do different compounding frequencies (monthly, quarterly, yearly) affect the present value?
4. Can you explain how compound interest differs from simple interest in these calculations?
5. How would a different time frame (e.g., 2 years for the first payment and 6 years for the second) affect the result?

**Tip:** When dealing with compound interest problems, always check the compounding frequency, as it significantly impacts the calculations.

What single payment today would replace a payment of $1,700.00 in 1 year and a payment of $3,900.00 in 5 years if the interest rate is 3.65% compounded quarterly?

Find the single payment today that would replace future payments of $1,700 in 1 year and $3,900 in 5 years, using a 3.65% interest rate compounded quarterly. This problem covers compound interest, present value, and time value of money, making it ideal for college-level students.

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