An annuit last for 12 calendar years.Atthe end of each quarter,there isa payment.First quarter paynments are $200,second quarter payments are $300,third quarter payments are $150 and fourth quarter payments ate $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 annuity:

A = PMT * [(1 + r)^n - 1] / r

where:
A = accumulated value of the annuity
PMT = payment made at the end of each quarter
r = nominal interest rate per period
n = number of periods

In this case, the quarterly payment amounts are given as follows:
First quarter payment: $200
Second quarter payment: $300
Third quarter payment: $150
Fourth quarter payment: $400

The nominal quarterly interest rate is 7.2% or 0.072, and the annuity lasts for 12 years, which means there are 48 quarters (12 years * 4 quarters).

Now, let's calculate the accumulated value:

First, we need to calculate the future value of each type of payment separately using the formula mentioned above.

For the first quarter payments:
PMT = $200
r = 0.072
n = 48
Using the formula,
Future value of first quarter payments = PMT * [(1 + r)^n - 1] / r

Next, we'll calculate the future value for each type of payment:

For the second quarter payments:
PMT = $300
r = 0.072
n = 48
Future value of second quarter payments = PMT * [(1 + r)^n - 1] / r

For the third quarter payments:
PMT = $150
r = 0.072
n = 48
Future value of third quarter payments = PMT * [(1 + r)^n - 1] / r

For the fourth quarter payments:
PMT = $400
r = 0.072
n = 48
Future value of fourth quarter payments = PMT * [(1 + r)^n - 1] / r

Finally, we add up the future values of all the payment types to get the accumulated value:

Accumulated value = Future value of first quarter payments + Future value of second quarter payments + Future value of third quarter payments + Future value of fourth quarter payments

By performing these calculations, we can find the accumulated value of the annuity just after the last payment.