Monarch Distributing Ltd. plans to accumulate funds for the purchase of a larger warehouse eight years from now. If Monarch contributes $12,000 at the beginning of each month to an investment account earning 4.5% compounded semiannually, what amount will Monarch accumulate by the end of the eight years?
To calculate the amount that Monarch Distributing Ltd. will accumulate over eight years, we need to use the formula for future value of an ordinary annuity.
The formula for the future value of an ordinary annuity is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value of the annuity
P is the monthly payment amount
r is the interest rate per period
n is the number of periods
In this case, Monarch makes monthly contributions of $12,000 for eight years, which is 8 * 12 = 96 periods. The interest rate is 4.5% compounded semiannually, so we need to calculate the interest rate per period.
The interest rate per period can be calculated by dividing the annual interest rate (4.5%) by the number of compounding periods per year (2).
Interest rate per period = 4.5% / 2 = 0.045 / 2 = 0.0225
Now we can substitute the values into the formula:
FV = 12000 * ((1 + 0.0225)^96 - 1) / 0.0225
We can simplify this expression using a calculator to get the final result.