Math Problem Statement
Given a 7 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $1,500, $1,700, $1,700, and $2,000, respectively.
Note: Do not round intermediate calculations and round your final answer to 2 decimal places.
Solution
To compute the present value (PV) of the payments, we use the formula for the present value of future payments:
Where:
- are the cash flows in years 1, 2, 3, and 4, respectively.
- is the interest rate (7% or 0.07).
- The denominator discounts each cash flow back to the present value.
Given the cash flows:
- Year 1:
- Year 2:
- Year 3:
- Year 4:
Substituting these into the formula and calculating the present value for each year:
Let's compute this step by step.The present value of the payments made in years 1, 2, 3, and 4 is $5,800.21.
Would you like more details on how this was calculated or have any further questions?
Here are 5 related questions to explore further:
- How would the present value change if the interest rate were 5% instead of 7%?
- How do you compute the future value of these cash flows at a 7% interest rate?
- What is the effect of increasing the number of payments on the present value?
- How does compounding frequency (monthly, quarterly, etc.) affect the present value of these payments?
- Can you compute the present value for varying interest rates over the four years?
Tip: When calculating the present value of future payments, ensure that you discount each payment based on the number of years it will take to receive that payment.
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Math Problem Analysis
Mathematical Concepts
Finance
Present Value
Discounting
Time Value of Money
Formulas
PV = C1 / (1 + r)^1 + C2 / (1 + r)^2 + C3 / (1 + r)^3 + C4 / (1 + r)^4
Theorems
Time Value of Money
Suitable Grade Level
College-level or Advanced High School (Finance or Economics course)
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