If you borrow $2,200 and agree to repay the loan in five equal annual payments at an interest rate of 12%, what will your payment be?

a. If you borrow $2,200 and agree to repay the loan in five equal annual payments at an interest rate of 12%, what will your payment be?

b. What will your payment be if you make the first payment on the loan immediately instead of at the end of the first year?

Explanation
Some values below may show as rounded for display purposes, though unrounded numbers should be used for actual calculations.

a.

PVOA	=	C((1 / r) – {1 / [r(1 + r)t]})
$1,000	=	C × ((1 / .12) – {1 / [.12(1.12)5]})
C	=	$610.30

b.

PVAD	=	[C((1 / r) – {1 / [r(1 + r)t]})] × (1 + r)
$1,000	=	C × ((1 / .12) – {1 / [.12(1.12)5]}) × 1.12
C	=	$544.91

You can also calculate this using the following:

PVAD	=	PVOA / (1 + r)
	=	$610.30 / 1.12
	=	$544.91

With the annuity due, you are paying each payment one year sooner which means that you will owe less interest on the loan. Thus, the annual loan payment with the annuity due will be less than the annual payment with the ordinary annuity.

Calculator computations:

Calculator payments set to "BGN".

Enter

5

12

–2,200

N

I/Y

PV

PMT

FV

Solve for

610.30

Calculator payments set to "BGN".

Enter

5

12

–2,200

N

I/Y

PV

PMT

FV

Solve for

544.91