Connie wants to have an annuity payment of $2,000 at the END of every three months. How much should she deposit now at 6% interest, compounded quarterly, to yield this payment for 3 years?
a) $21,815.02
To determine the amount Connie should deposit now to receive an annuity payment of $2,000 at the end of every three months for 3 years at a 6% interest rate compounded quarterly, we can follow these steps:
Step 1: Convert the interest rate to the quarterly rate.
Since the interest rate is given as 6% per year compounded quarterly, we need to divide it by 4 to get the quarterly rate. Therefore, the quarterly interest rate is 6% / 4 = 1.5%.
Step 2: Convert the time period to the number of quarters.
Since Connie wants the annuity payments for 3 years, and each payment is made every three months, we need to calculate the total number of quarters. There are 3 quarters in a year, so 3 years * 3 quarters per year = 9 quarters.
Step 3: Calculate the present value using the annuity formula.
The present value formula for an annuity is given by the equation:
PV = A * (1 - (1 + r)^(-n))/r
Where:
PV is the present value (the amount Connie needs to deposit)
A is the annuity payment ($2,000)
r is the quarterly interest rate (1.5% or 0.015 as a decimal)
n is the number of quarters (9).
Plugging in the values into the formula:
PV = 2000 * (1 - (1 + 0.015)^(-9))/0.015
Step 4: Solve the equation to find the present value.
Using a calculator or spreadsheet, calculate the value of the equation:
PV = 2000 * (1 - (1.015)^(-9))/0.015 ≈ $16,475.10
Therefore, Connie should deposit approximately $16,475.10 now to receive an annuity payment of $2,000 at the end of every three months for 3 years at a 6% interest rate compounded quarterly.