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14: Additional Examples 191
File name : English-M02-1-040308(Print).doc Print data : 2004/3/9
For instructions on entering Solver equations, see “Solving Your Own
Equations,” on page 29.
If you know the dates for the course of the loan, rather than the number
of days, use this for an actual-calendar basis:
or use this for a 360-day basis:
DATE1 = the date the loan commences.
DATE2 = the date the loan ends.
Yield of a Discounted (or Premium) Mortgage
The annual yield of a mortgage bought at a discount or premium can be
calculated given the original mortgage amount (
PV), interest rate (I%YR),
periodic payment (
PMT), balloon payment amount (if any) (FV), and the
price paid for the mortgage (new
PV).
Remember the cash-flow sign convention: money paid out is negative,
money received is positive.
Example: Discounted Mortgage. An investor wishes to purchase a
$100,000 mortgage taken out at 9% for 20 years. Since the mortgage
was issued, 42 monthly payments have been made. The loan is to be
paid in full (a
balloon payment) at the end of its fifth year. What is the
yield if the purchase price of the mortgage is $79,000?
1. Since the payment amount (
PMT) is not given, calculate it first. To
do this, first assume 20 years’ amortization on the original mortgage
with no balloon payment (so
N = 20 × 12, FV = 0, PV =－100,000,
and
I%YR = 9).
2. Since the balloon amount is not given, calculate it (
FV) next. Use PMT
from step 1, but change
N to 5 years (N = 5 × 12).