Mr. Norman will receive 8,500 a year for the next 15 years from her trust. If a 7 percent interest rate is applied, what is the current value of the future payments if first receipt occurs today?
To calculate the current value of future payments, we need to use the present value formula. The present value (PV) is equal to the future value (FV) divided by (1 + r/n)^(nt), where r is the interest rate, n is the number of compounding periods per year, and t is the number of years.
In this case, Mr. Norman will receive $8,500 every year for the next 15 years, and the interest rate is 7 percent.
To calculate the present value, let's plug in the values into the formula:
PV = $8,500 / (1 + 0.07/1)^(1*15)
Let's break down the formula:
- The interest rate is 7 percent, so we divide it by 1 (since we are compounding annually).
- The compounding periods per year (n) is 1, as mentioned above.
- The number of years (t) is 15.
- The future value (FV) is $8,500.
Now, let's calculate it:
PV = $8,500 / (1 + 0.07/1)^(1*15)
PV = $8,500 / (1 + 0.07)^(15)
PV = $8,500 / (1.07)^15
PV ≈ $5,242.75
The current value of the future payments, assuming the first receipt occurs today, is approximately $5,242.75.