VIPSolutionsGive step-by-step solution with explanation and final answer: {give the answer without using bulling-points} You will receive $50, 000 exactly 5 years from now. The discount rate is 8% per annum, compounded annually. What is the present value today? round to nearest whole number. Options A. $34, 027 B. $34,030 C. $34,045 D. $34, 100
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Give step-by-step solution with explanation and final answer: {give the answer without using bulling-points} You will receive $50, 000 exactly 5 years from now. The discount rate is 8% per annum, compounded annually. What is the present value today? round to nearest whole number. Options A. $34, 027 B. $34,030 C. $34,045 D. $34, 100
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Asked by: Francis
Created at: 2026-02-02 09:51:17
Asked by: Francis
Created at: 2026-02-02 09:51:17
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# Present Value of Future Cash Flow
We are given a future valueFV) of $50,000 to be received in 5 years, with a discount rate (r) of 8% per annum, compounded annually. We are to find the present value (PV) today.
## Step 1: Write the Present Value Formula
The formula for present value when compounding is annual:
\[
PV = \frac{FV}{(1 + r)^n}
\]
Where:
\( FV = \$50,000 \)
\( r = .08 \)
\( n = 5 \)
## Step 2: Substitute the Values
\[
PV = \frac{50,000}{(1 + .08)^5}
\]
\[
PV = \frac{50,000}{(1.08)^5}
\]
## Step 3: Calculate \((1.08)^5\)
\[
1.08^5 = 1.4693280768
\]
## Step 4: Calculate the Present Value
\[
PV = \frac{50,000}{1.4693280768}
\]
\[
PV \approx 34,027.03
\]
## Step 5: Round to the Nearest Whole Number
The present value rounded to the nearest dollar is $34,027.
## Final Answer
The correct answer is **A. $34,027**.
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