Problem

ind the present value of the given future amount.
$\$ 13,000$ for 15 months at $8 \%$ simple interest
What is the present value?
$\$$
(Round to the nearest dollar as needed.)

Answer

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Answer

Rounding to the nearest dollar, we get a final present value of \(\boxed{11818}\).

Steps

Step 1 :We are given a future value (FV) of $13,000, an interest rate of 8% per year, and a time period of 15 months. We are asked to find the present value (PV).

Step 2 :We can use the formula for simple interest to calculate the present value: \(PV = \frac{FV}{1 + r*n}\), where FV is the future value, r is the interest rate per period, and n is the number of periods.

Step 3 :First, we need to convert the annual interest rate to a monthly rate, since our time period is in months. We do this by dividing the annual rate by 12: \(r = \frac{8}{12} = 0.006666666666666667\).

Step 4 :Next, we plug in the given values into the formula: \(PV = \frac{13000}{1 + 0.006666666666666667*15}\).

Step 5 :Solving the equation gives us a present value of approximately $11818.181818181818.

Step 6 :Rounding to the nearest dollar, we get a final present value of \(\boxed{11818}\).

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