You

are

planning

to

purchase

a

car

that

costs

$30,000.

You

can

secure

a

loan

from

a

credit

union.

The

loan

officer

informed

you

of

the

loan

terms.

The

annual

percentage

rate

(APR)

is

6%,

and

the

loan

must

be

repaid

in

5

years.

What

will

be

your

monthly

payments

to

the

credit

union?

PVIFA

is

used

to

calculate

loan

payments.

Finance

Concept:

PV

=

PMT

*

PVIFA

r,t

=

PMT

[1-

(1/(1+r)

t

)

]

/

r

PMT

=

PV/

{

[1-(1/(1+r)

t

)]

/

r

}

We

"invert"

the

formula

for

PV

of

an

annuity,

and

solve

for

payment

or

cash

flows.

Numerical

Solution:

PV

=

PMT

*

PVIFA

r,t

30,000

=

PMT

*

[1-(1/(1+.06)

5

]/.06

30,000

=

PMT

*

[1-.74726]/.06

30,000

=

PMT

*

4.2124

PMT

=

30,000/4.2124

PMT

=

$7,121.83

with

calculator

In

Words:

The

yearly

payments

on

a

$30,000

loan

for

5

years

at

6%

are

$7,121.83

by

the

Wizard.

[The

difference

is

due

to

rounding

errors.]

Excel

Solution

for

Monthly

Payments: