Kenneth R. SzulczykAll loan payments are equal, so we set FV = FV 1 = FV 2 = FV 3 = ... = FVT. Thus, we can
factor the FV terms from all interest terms in Equation 22.ܸܲ=ܸܨቂ
ଵ
(ଵା)భ+
ଵ
(ଵା)మ+
ଵ
(ଵା)య+⋯+
ଵ
(ଵା)ቃ^ (^22 )^
We solve for FV, which becomes the loan payment, yielding Equation 23.ܸܨ=
బ
(భశభ)భା(భశభ)మା(భశభ)యା⋯ା(భశభ)൨
( 23 )
For example, a bank granted a mortgage for $60,000 at an interest rate of 12% APR.
Mortgage is a six-year loan and paid annually. We solve for FV and calculate your annual
payment of $14, 594 in Equation 24.ܸܨ=
,
ቂ(భశబభ.భమ)భା(భశబభ.భమ)మା(భశబభ.భమ)యା⋯ା(భశబభ.భమ)లቃ
( 24 )
ܸܨ=$14, 594
We can use the mortgage loan information to build an amortization table. We show an
amortization table in Table 9. For Year 0, you have $60,000 outstanding because you did not
make a payment yet. Then you make your first payment in Year 1. Your interest is 12%
multiplied by $60,000, equaling $7,200. If your payment is $14,594, then $7,200 is the interest
while the remainder reduces the principal. Thus, you subtract $7,394 from the loan balance. For
Year 2, and beyond, you repeat the sequence until you pay the loan in full in Year 6.Table 9. An Amortization TablePayment Interest Principal Paid Loan Balance
Year 0 - - - $60,000
Year 1 $14,594 $7,200 $7,394 $52,606
Year 2 $14,594 $6,313 $8,281 $44,325
Year 3 $14,594 $5,319 $9,275 $35,050
Year 4 $14,594 $4,206 $10,388 $24,662
Year 5 $14,594 $2,959 $11,635 $13,027
Year 6 $14,594 $1,563 $13,027 $0
All amortization tables have one feature. First payment has the highest interest while the
lowest principal applied to the loan balance. Then the interest amount declines over the life of
the loan until it becomes the smallest for the last payment.
If a mortgage is monthly, then you divide the interest rate by 12 and multiply the number of
years by 12. For instance, a 20-year mortgage will have 240 payments, 12 × 20. As you can see,