Multiple Choice
If you deposit \(1,000 into a savings account that earns 10\% annual interest compounded annually, how many years will it take for your investment to grow to \)2,000?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the present value (PV) of the following set of cash flows, discounted at an annual rate of 8\%? - Year 1: \$1,000- Year 2: \$1,500- Year 3: \$2,000\[PV = \frac{1,000}{(1+0.08)^1} + \frac{1,500}{(1+0.08)^2} + \frac{2,000}{(1+0.08)^3}\]Which of the following is closest to the correct present value?
A
\$4,200
B
\$4,011
C
\$3,870
D
\$4,000
Verified step by step guidance1
Step 1: Understand the concept of Present Value (PV). PV is the current worth of future cash flows discounted at a specific rate. The formula for PV is \( PV = \frac{CF}{(1 + r)^n} \), where CF is the cash flow, r is the discount rate, and n is the year.
Step 2: Break down the problem into individual cash flows. For Year 1, the cash flow is \$1,000, for Year 2 it is \$1,500, and for Year 3 it is \$2,000. The discount rate is 8\% (or 0.08).
Step 3: Apply the PV formula to each cash flow. For Year 1, calculate \( PV_1 = \frac{1,000}{(1 + 0.08)^1} \). For Year 2, calculate \( PV_2 = \frac{1,500}{(1 + 0.08)^2} \). For Year 3, calculate \( PV_3 = \frac{2,000}{(1 + 0.08)^3} \).
Step 4: Add the present values of all cash flows together to find the total present value. \( PV_{total} = PV_1 + PV_2 + PV_3 \).
Step 5: Compare the calculated total present value to the given options (\$4,200, \$4,011, \$3,870, \$4,000) to determine which is closest to the correct answer.
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