here is the question:

An annuity pays 100 at the end of each month for 20 years. Using a nominal rate of interest of 4% compounded quarterly, calculate the current value of the annuity at the end of the 3rd year.

Ok, so I found a present value of 16,521.23 (calculated a monthly interest rate of.33222835%)

Now, in my understanding, to find the current value of the annuity at the end of the 3rd year, you would take the present value of the remaining payments (in this case, 204). The correct answer is $18,616.53, which is what you get when you take 16,521.23 and multiply it by (1.0033222835^36).

Why is this the answer? Doesn't the value of the annuity decrease as each payment is made, eventually becoming zero when the last payment is made? Or do I have it backwards?

An annuity pays 100 at the end of each month for 20 years. Using a nominal rate of interest of 4% compounded quarterly, calculate the current value of the annuity at the end of the 3rd year.

Ok, so I found a present value of 16,521.23 (calculated a monthly interest rate of.33222835%)

Now, in my understanding, to find the current value of the annuity at the end of the 3rd year, you would take the present value of the remaining payments (in this case, 204). The correct answer is $18,616.53, which is what you get when you take 16,521.23 and multiply it by (1.0033222835^36).

Why is this the answer? Doesn't the value of the annuity decrease as each payment is made, eventually becoming zero when the last payment is made? Or do I have it backwards?

## Comment