Just like how we calculated the present value of future
annuity payments now, we can calculate the vice versa meaning we can calculate
the future value of cash flow payments (PMT) given a present value today.
Remember in these calculations, we do not need the Future value (FV) information.
Let’s take an example; suppose you want to start up a new business
and need $100,000 to start up, market and run your business. Because you
feel the business will be short lived for some reason, you would like
to pay off this $100,000 balance in a set of five equal payments. Given
the interest rate is 14%, what will your monthly annuity payments (five
of them) be?
Notice in this example we know the present value is $100,000
and the interest rate on the loan is 14%. Since these payments are spread
over 5 periods and the payments will be equal, what will the payments
be? We will use the present value of an annuity formula to derive our
answer:
Annuity Present Value = C x [(1
– Present Value Factor) / r]
$100,000 = C x [(1 – $1/
(1 + r)t) / r]
$100,000 = C x [(1 – $1/
(1 + 0.14)5) / 0.14]
$100,000 = C x [(1 – $1/
(1.93) / 0.14]
$100,000 = C x [(1 – 0.518)
/ 0.14]
$100,000 = C x [(0.482) / 0.14]
$100,000 = C x 3.443
C = $100,000 / 3.443
C = $29,044.44
This therefore means you will have to make annuity payments
of $29,044.44 every year for the next 5 years to pay off the $100,000
loan at 14% interest rate.
Here’s how to do this exact calculation using our
BAII plus financial calculator:
Find annuity PMTs of $100,000 PV at Year 5, 14% borrowing
rate using our Financial Calculator
N
=
5
I/Y =
14%
PV =
$-100,000
PMT =
?
FV =
$0
2ND
I/Y
P/Y =
1
C/Y =
1
CPT & PV =
$29,128.35
Below is a graphical representation of this data.
This graph above shows the equal annual payments
of $29,044.44 that will pay off the entire loan in 5 years at 14% interest
rate. The graph also indicates to us that the total cost of the loan would
be $145,222.20 which indicates total interest will be $145,222.20 - $100,000
= $45,222.20
