Final answer:
To calculate the present value of a stream of payments with a 5% interest discount rate, we use the present value formula. We calculate the present value of each payment and then sum them to find the total present value. In this case, the stream of payments is worth $2,164.65 today.
Step-by-step explanation:
To calculate the present value of a stream of payments, we need to discount each payment back to the present using the interest rate. In this case, the interest discount rate is 5% compounded annually.
Since the stream of payments is received for five years, we need to calculate the present value of each payment and then add them up. Using the formula for present value of an annuity:
PV = C / (1 + r)^n
where PV is the present value, C is the payment, r is the interest rate, and n is the number of years:
- For the first payment of $500 at the end of year 1, the present value is $500 / (1 + 0.05)^1 = $476.19
- For the second payment of $500 at the end of year 2, the present value is $500 / (1 + 0.05)^2 = $453.51
- For the third payment of $500 at the end of year 3, the present value is $500 / (1 + 0.05)^3 = $431.93
- For the fourth payment of $500 at the end of year 4, the present value is $500 / (1 + 0.05)^4 = $411.35
- For the fifth and final payment of $500 at the end of year 5, the present value is $500 / (1 + 0.05)^5 = $391.67
Finally, we add up all the present values to find the total present value of the stream of payments:
Total present value = $476.19 + $453.51 + $431.93 + $411.35 + $391.67 = $2,164.65