What is the present value of an investment that will be worth $2000 at the end of five years? Assume an APR (Annual Percentage Rate) of 6% compounded monthly.
The present value is $_____ .
P = Po(1+r)^n = 2000
r = (6%/12)/100% = 0.005
n = 12comp/yr. * 5yrs. = 60 compounding
periods.
Po(1.005)^60 = 2000
Po = 2000/(1.005^60) = $1482.74=Initial
deposit or present value.
To find the present value of an investment, we need to use the formula for calculating the future value of an investment and rearrange it. The formula for calculating the future value of an investment with compound interest is:
FV = PV * (1 + r/n)^(n*t)
Where:
- FV represents the future value of the investment.
- PV represents the present value of the investment.
- r represents the annual interest rate (APR).
- n represents the number of times that interest is compounded per year.
- t represents the number of years.
To find the present value, we rearrange the formula as follows:
PV = FV / (1 + r/n)^(n*t)
Now, let's substitute the given values into the formula:
FV = $2000
r = 6% = 0.06 (as a decimal)
n = 12 (monthly compounding)
t = 5 years
PV = $2000 / (1 + 0.06/12)^(12*5)
To calculate this equation, we evaluate the expression in parentheses first:
PV = $2000 / (1 + 0.005)^(60)
Next, we simplify the exponent:
PV = $2000 / (1.005)^(60)
Finally, we calculate the result:
PV ≈ $2000 / 1.348090
Therefore, the present value of the investment is approximately $1484.80.