Jean will receive $8,500 per year for the next 15 years from her trust. If a 7% interest rate is applied, what is the current value of the future payments? I get a rounded sum of $200,180.
PV = 8500( 1 - 1.07^-15)/.07
= $77,417.27
I have no idea how you got your answer.
If we had found the value of her trust fund at the end of 15 years it would have been
8500( 1.07^15 - 1)/.07 = $213,596.69
Proof:
Time interest withdrawal balance
------------------------77,417.27
1 5419.2089 8500 74,336.48
2 5203.553523 8500 71,040.03
3 4972.80227 8500 67,512.83
4 4725.898428 8500 63,738.73
5 4461.711318 8500 59,700.44
6 4179.031111 8500 55,379.48
7 3876.563289 8500 50,756.04
8 3552.922719 8500 45,808.96
9 3206.627309 8500 40,515.59
10 2836.091221 8500 34,851.68
11 2439.617606 8500 28,791.30
12 2015.390839 8500 22,306.69
13 1561.468197 8500 15,368.16
14 1075.770971 8500 7,943.93
15 556.074939 8500 0 0.00
Well, those numbers did not line up nicely at all
should have formatted to 2 decimal places ...
The first row would be
1 -- 5419.21 -- 8500 -- 74,336.48
but you can see that after the last payment of $8500, the balance is 0.00
(above done on Excel , and then cut and pasted.)
To calculate the current value of future payments, you need to use the concept of present value. This involves discounting the future payments to account for the time value of money. Here's how to calculate it step by step:
1. Determine the annual payment amount: In this case, Jean will receive $8,500 per year for the next 15 years.
2. Determine the interest rate: The interest rate given is 7%, which needs to be converted to a decimal by dividing it by 100 (7/100 = 0.07).
3. Calculate the present value factor: To convert the future payments to their equivalent current value, you need to use a present value factor. This factor depends on both the interest rate and the number of periods. The formula to calculate the present value factor is: PV factor = 1 / (1 + r)^n, where r is the interest rate and n is the number of periods.
4. Calculate the present value of each future payment: Multiply the annual payment amount ($8,500) by the present value factor for each year. This accounts for the decreasing value of future payments due to discounting.
5. Sum up all the present values: Add up the present values of each future payment to determine the total current value.
Using these steps, let's calculate the present value:
PV factor = 1 / (1 + 0.07)^15
PV factor ≈ 0.391
Present value = $8,500 × 0.391 (rounded to two decimal places)
Calculating the present value for each year:
Year 1: $8,500 × 0.391 = $3,316.35
Year 2: $8,500 × 0.391 = $3,316.35
...
Year 15: $8,500 × 0.391 = $3,316.35
Total present value = $3,316.35 × 15 = $49,745.25
Based on these calculations, the present value of the future payments is approximately $49,745.25. This is different from the rounded sum you mentioned, so there may be a discrepancy in the calculations. Double-checking the calculations can help identify any errors.