What is the present value of an investment that will be worth $ 3000$ 3000 at the end of five years? Assume an APR of 6% compounded monthly.
P = Po(1+r)^n = $3,000.
r = 0.06/12mo. = 005/mo.
n = 12Comp./yr. * 5yrs. = 60 Compounding periods.
Po(1.005)^60 = 3000, Po = ?.
To calculate the present value of an investment, we need to use the formula for the present value of a future sum of money.
The formula to calculate the present value is:
\[PV = \dfrac{FV}{(1+r/n)^{nt}}\]
Where:
- PV is the present value (the amount we want to find)
- FV is the future value (given as $3000)
- r is the annual percentage rate (APR) divided by the number of compounding periods (compounded monthly in this case)
- n is the number of compounding periods per year (12 for monthly compounding)
- t is the number of years (given as 5)
Let's plug in the values into the formula and calculate the present value.
Using the given values:
- FV = $3000
- APR = 6%, which means r = 0.06
- n = 12 (monthly compounding)
- t = 5
\[PV = \dfrac{3000}{(1+0.06/12)^{12*5}}\]
Simplifying further:
\[PV = \dfrac{3000}{(1+0.005)^{60}}\]
Using a calculator, we can evaluate this expression to find the present value. The value of the expression is approximately $2,531.39.
Therefore, the present value of the investment that will be worth $3000 at the end of five years, with an APR of 6% compounded monthly, is approximately $2,531.39.