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
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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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