Question

Someone wants to have 15000 in 3 years to start a business, and they plan to save the money by making regular deposits into an annuity that earns 4.8% compounded monthly. What monthly deposits does this person need to make?

Answer 1

To have $15,000 in 3 years with an account earning 4.8% compounded monthly, monthly deposits of approximately $393.35 are required.

Step-by-step explanation:

To reach a goal of $15,000 in 3 years with an annuity that earns 4.8% annual interest compounded monthly, we need to calculate the necessary monthly deposits. The future value of an annuity formula considering monthly compounding needs to be rearranged to solve for the monthly payment (PMT).

The formula is:

FV = PMT * (((1 + r/n)^(nt) - 1) / (r/n))

Where:

• FV is the future value of the annuity, which is $15,000.
• PMT is the monthly payment we need to find.
• r is the annual interest rate (4.8%), expressed as a decimal (0.048).
• n is the number of times the interest is compounded per year, which is 12.
• t is the number of years, which is 3.

By rearranging the formula, we have:

PMT = FV / (((1 + r/n)^(nt) - 1) / (r/n))

Plugging in the known values:

PMT = $15,000 / (((1 + 0.048/12)^(12*3) - 1) / (0.048/12))

After calculating, we find that the monthly deposits required to achieve this goal are approximately $393.35.