An annuity last for 12 calendar years.At the end of each quarter,there is a payment.First quarter payments 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%.
Start with m = 200(1+I)^3 +300(1+I)^2+150(1+I)+400
To find the accumulated value of the annuity just after the last payment, we need to calculate the future value of each payment and then sum them up.
First, let's calculate the future value of each payment using the formula for the future value of an ordinary annuity:
Future Value = Payment * ((1 + Interest Rate)^Number of Periods - 1) / Interest Rate
For the first quarter payment of $200, the number of quarters is 12 (since the annuity lasts for 12 years) and the interest rate is 7.2% per quarter. Plugging in these values into the formula:
FV1 = $200 * ((1 + 0.072)^12 - 1) / 0.072 = $200 * (1.968246 - 1) / 0.072 = $200 * 0.968246 / 0.072 = $2,682.92
For the second quarter payment of $300, the number of quarters is 12, and using the same interest rate:
FV2 = $300 * ((1 + 0.072)^12 - 1) / 0.072 = $300 * (1.968246 - 1) / 0.072 = $300 * 0.968246 / 0.072 = $4,024.38
For the third quarter payment of $150:
FV3 = $150 * ((1 + 0.072)^12 - 1) / 0.072 = $150 * (1.968246 - 1) / 0.072 = $150 * 0.968246 / 0.072 = $2,012.19
And finally, for the fourth quarter payment of $400:
FV4 = $400 * ((1 + 0.072)^12 - 1) / 0.072 = $400 * (1.968246 - 1) / 0.072 = $400 * 0.968246 / 0.072 = $5,364.92
Now, we can sum up these future values to find the accumulated value of the annuity just after the last payment:
Accumulated Value = FV1 + FV2 + FV3 + FV4 = $2,682.92 + $4,024.38 + $2,012.19 + $5,364.92 = $14,084.41
Therefore, the accumulated value of this annuity just after the last payment is $14,084.41.