Final answer:
The monthly payment required for a business to accumulate $75,000 over 12 years with an investment earning 7.8% interest compounded monthly can be calculated using the future value of an annuity formula, with the payment P being the unknown variable to solve for.
Step-by-step explanation:
To calculate the size of each monthly payment needed to accumulate $75,000 in 12 years with an investment account that has an annual interest rate of 7.8% compounded monthly, we would use the future value of an annuity formula. The formula for the future value of an annuity compounded monthly is given by:
FV = P * [((1 + r/n)^(nt) - 1) / (r/n)]
Where:
FV is the future value of the annuity,
P is the monthly payment,
r is the annual interest rate in decimal form,
n is the number of compounds per year,
t is the number of years.
To find the monthly payment P, we need to rearrange the formula to solve for P, given that FV is $75,000, r is 0.078, n is 12 (since the interest is compounded monthly), and t is 12 years:
P = FV / [((1 + r/n)^(nt) - 1) / (r/n)]
Filling in the values, we get the monthly payment P. Remember to round the final calculation to two decimal places, as required by the question.