QuestionAugust 21, 2025

Liam would receive 8,000 every year for six years. The rate of interest is 8% What would be the present value of the amount that would be received by Liam at the end of six years? C 38,000.00 37,500.00 37,200.00 37,040.00

Liam would receive 8,000 every year for six years. The rate of interest is 8% What would be the present value of the amount that would be received by Liam at the end of six years? C 38,000.00 37,500.00 37,200.00 37,040.00
Liam would receive 8,000 every year for six years. The rate of interest is
8%  What would be the present value of the amount that would be received
by Liam at the end of six years?
C 38,000.00
 37,500.00
 37,200.00
 37,040.00

Solution
4.3(355 votes)

Answer

\36,983.04 Explanation 1. Identify the Present Value Formula Use the formula for the present value of an annuity: **PV = C \times \frac{1 - (1 + r)^{-n}}{r}**, where C is the annual cash flow, r is the interest rate, and n is the number of periods. 2. Substitute Values into the Formula Here, C = 8000, r = 0.08, and n = 6. Substitute these values into the formula: PV = 8000 \times \frac{1 - (1 + 0.08)^{-6}}{0.08}. 3. Calculate the Present Value Compute PV = 8000 \times \frac{1 - (1.08)^{-6}}{0.08} = 8000 \times \frac{1 - 0.63017}{0.08} = 8000 \times 4.62288. 4. Final Calculation Multiply to find PV = 36983.04.

Explanation

1. Identify the Present Value Formula<br /> Use the formula for the present value of an annuity: **$PV = C \times \frac{1 - (1 + r)^{-n}}{r}$**, where $C$ is the annual cash flow, $r$ is the interest rate, and $n$ is the number of periods.<br /><br />2. Substitute Values into the Formula<br /> Here, $C = 8000$, $r = 0.08$, and $n = 6$. Substitute these values into the formula: $PV = 8000 \times \frac{1 - (1 + 0.08)^{-6}}{0.08}$.<br /><br />3. Calculate the Present Value<br /> Compute $PV = 8000 \times \frac{1 - (1.08)^{-6}}{0.08} = 8000 \times \frac{1 - 0.63017}{0.08} = 8000 \times 4.62288$.<br /><br />4. Final Calculation<br /> Multiply to find $PV = 36983.04$.
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