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? Describe how you solved this problem, including which table (for example, present value and future value) was used and why.
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? Describe how you solved this problem, including which table (for example, present value and future value) was used and why.
To determine the current value of the future payments, we can use the present value of an ordinary annuity formula.
The formula for calculating the present value of an ordinary annuity is:
PV = PMT x (1 - (1 + r)^(-n)) / r
Where:
PV = Present Value
PMT = Periodic payment
r = Interest rate per period
n = Number of periods
In this case, Jean will receive $8,500 per year for the next 15 years, and the interest rate is 7%.
Substituting these values into the formula, we have:
PV = $8,500 x (1 - (1 + 0.07)^(-15)) / 0.07
Now, we can calculate the present value using the formula.
PV = $8,500 x (1 - (1.07)^(-15)) / 0.07
= $8,500 x (1 - 0.209383082) / 0.07
= $8,500 x (0.790616918) / 0.07
= $8,500 x 11.2945274
= $95,997.48
Therefore, the current value of the future payments is approximately $95,997.48.
To solve this problem, we used the present value formula because we need to find the present value of the future payments. The present value represents the current worth of a series of future cash flows, taking into account the time value of money.
To solve this problem, we need to calculate the present value of future payments. This can be done using the present value of an ordinary annuity formula:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
where:
PV = Present Value
PMT = Annual payment amount
r = Interest rate per period
n = Number of periods
In this case, Jean will receive $8,500 per year for the next 15 years, and the interest rate is 7%.
So, we plug in the values into the formula:
PV = $8,500 × [(1 - (1 + 0.07)^(-15)) / 0.07]
Now let's calculate the present value step by step:
1. Calculate the value inside the square brackets:
(1 + 0.07)^(-15) ≈ 0.4526 (using a calculator or Excel)
2. Calculate the numerator:
1 - 0.4526 ≈ 0.5474
3. Divide the numerator by the interest rate:
0.5474 / 0.07 ≈ 7.82
4. Multiply the result by the annual payment amount:
$8,500 × 7.82 ≈ $66,370
Therefore, the current value (present value) of the future payments is approximately $66,370.
In this calculation, we used the present value table because we needed to find the current value of future cash flows (the future payments) based on the interest rate. The present value table helps us calculate the present value of an ordinary annuity quickly and accurately. However, it's important to note that you can also use financial calculators or software that have built-in formulas to find the present value directly without using tables.