Principles of Managerial Finance

Loan Amortization

The termloan amortizationrefers to the computation of equal periodic loan pay-

ments. These payments provide a lender with a specified interest return and

repay the loan principal over a specified period. The loan amortization process

involves finding the future payments, over the term of the loan, whose present

value at the loan interest rate equals the amount of initial principal borrowed.

Lenders use aloan amortization scheduleto determine these payment amounts

and the allocation of each payment to interest and principal. In the case of home

mortgages, these tables are used to find the equalmonthlypayments necessary to

amortize,or pay off, the mortgage at a specified interest rate over a 15- to 30-

year period.

Amortizing a loan actually involves creating an annuity out of a present

amount. For example, say you borrow $6,000 at 10 percent and agree to make

equal annual end-of-year payments over 4 years. To find the size of the payments,

the lender determines the amount of a 4-year annuity discounted at 10 percent

that has a present value of $6,000. This process is actually the inverse of finding

the present value of an annuity.

Earlier in the chapter, we found the present value, PVAn, of an n-year annu-

ity by multiplying the annual amount, PMT,by the present value interest factor

for an annuity, PVIFAi,n. This relationship, which was originally expressed as

Equation 4.16, is repeated here as Equation 4.26:

PVAnPMT(PVIFAi,n) (4.26)

loan amortization
The determination of the equal
periodic loan payments
necessary to provide a lender
with a specified interest return
and to repay the loan principal
over a specified period.

loan amortization schedule
A schedule of equal payments to
repay a loan. It shows the alloca-
tion of each loan payment to
interest and principal.

CHAPTER 4 Time Value of Money 183

3547.93

20,000 FV

N

CPT

PMT

I

5

6

Solution

Input Function

FVA 5 $20,000 and FVIFA6%,5yrs5.637 into Equation 4.25 yields an annual

required deposit, PMT,of $3,547.99. Thus if $3,547.99 is deposited at the end of

each year for 5 years at 6% interest, there will be $20,000 in the account at the

end of the 5 years.

Calculator Use Using the calculator inputs shown at the left, you will find the

annual deposit amount to be $3,547.93. Note that this value, except for a slight

rounding difference, agrees with the value found by using Table A–3.

Spreadsheet Use The annual deposit needed to accumulate the future sum also

can be calculated as shown on the following Excel spreadsheet.