Suppose that you desire to get a lump-sum payment of $100,000 two years from now. How many current dollars will you have to invest today at 12 percent interest to accomplish your goal?Instructions: Round your answer to the nearest dollar.$
Question
Suppose that you desire to get a lump-sum payment of
Solution
To calculate the amount of money you need to invest today to get a lump-sum payment of $100,000 two years from now at 12 percent interest, you can use the formula for the present value of a future sum in finance. The formula is:
PV = FV / (1 + r)^n
where:
- PV is the present value, or the amount of money you need to invest today.
- FV is the future value, or the lump-sum payment you want to get, which is $100,000.
- r is the interest rate, which is 12 percent or 0.12.
- n is the number of periods, which is 2 years.
Substituting the values into the formula, we get:
PV = $100,000 / (1 + 0.12)^2
Now, calculate the denominator:
1 + 0.12 = 1.12 1.12^2 = 1.2544
Then, divide the future value by this result:
PV = $100,000 / 1.2544
Finally, round your answer to the nearest dollar to get the amount of money you need to invest today.
PV = $79,719
So, you need to invest approximately 100,000 two years from now at 12 percent interest.
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