If you put up $39,000 today in exchange for a 6.5 percent, 16-year annuity, what will the annual cash flow be?

Problem 6-5 Calculating Annuity Cash Flows [LO1]

If you put up $39,000 today in exchange for a 6.5 percent, 16-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									16
$39,000	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 = $39,000 = $C{[1 − (1 / 1.065016)] / .0650}

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

C = $39,000 / 9.767764

C = $3,992.73

   

Calculator Solution:

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

   
 

Enter

16

6.50%

$39,000

N

I/Y

PV

PMT

FV

Solve for

$3,992.73