If you put up $51,000 today in exchange for a 6.25 percent, 15-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

If you put up $51,000 today in exchange for a 6.25 percent, 15-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

 

Annual cash flow

$

 

Explanation:

The time line is:

0	1									15
$51,000	C	C	C	C		C	C	C	C	C

Here we have the PVA, the length of the annuity, and the interest rate. We want to calculate the annuity payment. Using the PVA equation:

PVA = C({1 − [1 / (1 + r)t]} / r)

PVA = $51,000 = $C{[1 − (1 / 1.062515)] / .0625}

We can now solve this equation for the annuity payment. Doing so, we get:

C = $51,000 / 9.555549

C = $5,337.21

   

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

   
 

Enter

15

6.25%

$51,000

N

I/Y

PV

PMT

FV

Solve for

$5,337.21