Question

How much should Kimberly's dad invest into a savings account today, to be able to pay for Kimberly's rent for the next six years if rent is $750 payable at the beginning of each month? The savings account earns 3.50% compounded monthly. Round to the nearest cent For 32 years, Janet saved $250 at the beginning of every month in a fund that earned 4.67% compounded annually. a. What was the balance in the fund at the end of the period? Round to the nearest cent

Answer 1

To cover six years of rent at $750 per month with an account earning 3.50% interest compounded monthly, Kimberly's dad needs to calculate the present value of an annuity due. Likewise, to determine the balance of Janet's savings after 32 years of monthly $250 deposits at 4.67% interest compounded annually, the future value of an annuity formula should be used.

Step-by-step explanation:

To determine how much Kimberly's dad should invest today to pay for her rent over the next six years with rent being $750 per month and the savings account earning 3.50% interest compounded monthly, we use the formula for the present value of an annuity due:

PV = R * [(1 - (1 + i)^-nt) / i] * (1+i)

Where PV is the present value, R is the monthly rent, i is the monthly interest rate, n is the number of compounds per year, and nt is the total number of compounding periods.

For Janet's balance after saving for 32 years with a monthly deposit of $250 and an annual interest rate of 4.67% compounded annually, we use the future value formula for an annuity:

FV = R * [((1 + i)^nt - 1) / i] * (1+i)

Where FV is the future value, R is the monthly deposit, i is the annual interest rate, n is the number of times interest is compounded per year (which is 1 for annually), and nt is the total number of compounding periods.