You are the owner of a Jani-King cleaning service franchise. Your accountant has determined that your business will need $27,500 in new equipment in 3 years. If your bank is paying 6% interest compounded monthly, how much must you invest today to meet this financial goal? (Round to the nearest whole dollar.)
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To determine how much you must invest today to meet the financial goal, you can use the formula for the future value of a present sum of money:
FV = PV * (1 + r/n)^(nt)
Where:
FV = future value
PV = present value (amount you need to invest today)
r = annual interest rate (expressed as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, the future value (FV) is $27,500, the annual interest rate (r) is 6% (or 0.06 as a decimal), the interest is compounded monthly (n = 12), and the investment period (t) is 3 years.
Plugging the values into the formula:
$27,500 = PV * (1 + 0.06/12)^(12 * 3)
Simplifying the equation:
$27,500 = PV * (1 + 0.005)^36
Now, divide both sides of the equation by (1 + 0.005)^36:
$27,500 / (1 + 0.005)^36 = PV
Calculating the value on the right side gives you:
$27,500 / (1.005)^36 = PV
Using a calculator:
$27,500 / 1.218994 = PV
PV ≈ $22,558.93
Therefore, you would need to invest approximately $22,558.93 today to meet your financial goal of $27,500 in 3 years, considering a 6% interest compounded monthly.