An annuity last for 12 calendar years.At the end of each quarter,there is a payment.First quarter payment are $200,second quarter payments are $300,third quarter payments are $150 and fourth quarter payments are $400.Find the accumulated value of this annuity just after the last payment using a nominal quarterly interest rate of 7.2%.
To find the accumulated value of the annuity just after the last payment, we can use the formula for the future value of an ordinary annuity.
First, we need to determine the number of quarters in 12 calendar years. Since there are 4 quarters in a year, the annuity will last for 12 * 4 = 48 quarters.
Next, we need to calculate the future value of each quarterly payment using the formula:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future Value
P = Payment per period
r = Interest rate per period
n = Number of periods
Let's calculate the future value for each quarter payment:
For the first quarter payment of $200 with a nominal quarterly interest rate of 7.2%, we have:
FV1 = $200 * ((1 + 0.072)^48 - 1) / 0.072
For the second quarter payment of $300:
FV2 = $300 * ((1 + 0.072)^47 - 1) / 0.072
For the third quarter payment of $150:
FV3 = $150 * ((1 + 0.072)^46 - 1) / 0.072
For the fourth quarter payment of $400:
FV4 = $400 * ((1 + 0.072)^45 - 1) / 0.072
Now, we can calculate the accumulated value of the annuity just after the last payment by summing up the future values of each payment:
Accumulated Value = FV1 + FV2 + FV3 + FV4
Simply plug in the values and calculate to get the result.