Jerry will receive the following payments: 946 in year 3, 929 in year 5 and 958 in year 9. What is the purchasing power of the present value of these payments if the market interest rate is 17% per year and the inflation rate is 6% per year?
To calculate the purchasing power of the present value of these payments, we need to find the present value of each payment and then consider the effects of inflation. Here's how you can calculate it step by step:
1. Calculate the present value of each payment:
To find the present value, you can use the formula for the present value of a single sum. PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods.
For the first payment of $946 in year 3:
PV1 = 946 / (1 + 0.17)^3
For the second payment of $929 in year 5:
PV2 = 929 / (1 + 0.17)^5
For the third payment of $958 in year 9:
PV3 = 958 / (1 + 0.17)^9
2. Adjust for inflation:
Inflation reduces the purchasing power of money over time. To adjust for inflation, we need to find the inflated present value of each payment. This can be done by dividing the present value by (1 + inflation rate)^n.
For example, let's assume the inflation rate is 6% per year. We'll use the same formula as before, but this time, we divide by (1 + 0.06)^n:
Inflated PV1 = PV1 / (1 + 0.06)^3
Inflated PV2 = PV2 / (1 + 0.06)^5
Inflated PV3 = PV3 / (1 + 0.06)^9
3. Calculate the total purchasing power of the present value:
To find the total purchasing power, simply add up the inflated present values of each payment.
Total Purchasing Power = Inflated PV1 + Inflated PV2 + Inflated PV3
By following these steps and plugging in the values, you can find the purchasing power of the present value of these payments.