Question

Maria needs to invest to help with her child's college fund. How much would she have to invest to have $79,400 after 12 years, assuming an interest rate of 2.12% compounded daily? Do not round any intermediate computations, and round your final answer to the nearest dollar. If necessary, refer to the list of financial formulas. Assume there are 365 days in each year.

Answer 1

To find out how much Maria needs to invest for her child's college fund, the present value is calculated using the compound interest formula, considering a 2.12% interest rate compounded daily for 12 years.

Step-by-step explanation:

Maria is looking to invest for her child's college fund and needs to know how much to invest to have $79,400 after 12 years with an interest rate of 2.12% compounded daily. To calculate the present value (PV) of her future investment, the formula for compound interest is used:

PV = FV / (1 + r/n)nt

Where:

• FV = Future Value ($79,400)
• r = annual interest rate (0.0212)
• n = number of times the interest is compounded per year (365)
• t = number of years the money is invested (12)

Substituting these values into the formula, we get:

PV = 79,400 / (1 + 0.0212/365)365*12

Calculating this will determine the amount Maria needs to initially invest. It is crucial to compound interest calculation to not round intermediate computations for accuracy. Once computed, the present value is rounded to the nearest dollar representing the initial investment required.