Question

Calculate the amount of money Kayla had to deposit in an investment fund growing at an interest rate of 4.00% compounded annually, to provide his daughter with $12,000 at the end of every year, for 5 years, throughout undergraduate studies. Round to the nearest cent

Answer 1

To calculate the present value that Kayla needs to deposit in an investment fund with a 4% annual compound interest rate to provide $12,000 each year for 5 years, we use the present value of an annuity formula.

Step-by-step explanation:

The question at hand involves determining the initial deposit that Kayla would need to make into an investment fund with a 4.00% annual compound interest rate to provide $12,000 each year for her daughter for 5 years. This is a present value of an annuity problem, where the periodic payment (annuity) is $12,000, and the interest rate is 4% per annum.

To calculate the present value (PV) of an annuity, we use the formula:

PV = Pmt * [(1 - (1 + r)^(-n)) / r]

Where:

• Pmt is the annuity payment per period ($12,000)
• r is the interest rate per period (0.04)
• n is the number of periods (5)

Let's plug in the values:

PV = $12,000 * [(1 - (1 + 0.04)^(-5)) / 0.04]

After performing the calculations, don't forget to round the final answer to the nearest cent, as specified in the question.

Note: The provided examples talk about compound interest and show how a sum of money can grow over time when invested. This concept is related to Kayla's question but with a different interest rate and different financial goal.