Mortgage Math. Fixed-Rate Mortgage Calculations Payments Balances Yields Annual Nominal Rate APR True Annual Nominal Rate Effective Yields. Fixed-Rate Mortgages. Let’s look at this mortgage in terms of “time value of money” principles 1. The borrower’s payments are a simple annuity.
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Calculate the required payment if maturity is 30 years, interest rate is 8% and principal is $150,000
N=360 months
i=8%/12=.66667
PV=-150,000
PMT=$1,100.65
Calculate the maximum loan size you can borrow if you can pay $1000 per month, the interest rate is 7.5%, and the maturity is 25 years.
N=25*12=300months
PMT=$1000
i=7.5/12=.6250
PV=$135,319.61
Calculate the maturity of a loan if the monthly payment is $843.86, the principal balance is $100,000 and the interest rate is 6%
i=6/12=.5
PV=-100,000
PMT=843.66
N=??? (180 months)
Calculate the interest rate of a loan if the principal amount of the loan is $175,000, the monthly payment is $1,367.36 and the maturity of the loan is 30 years.
N=30*12=360
PMT=$1,367.36
PV=-175,000
i=??? (.72292% /month)
8.675%/year
Amortization Schedule for 8% 30 Year FRM
Paydown Pattern of 8% Fixed Rate Mortgage
Components of Payment
Formulas For Calculating Payment in EXCEL
Column I
Column H
Note that EXCEL wants the interest rate in decimal form.
Formulas for Amortizing Loan
Column F
Column B
Column C
Column D
Column E
Row
2
3
4
Amortization Schedule for 8% 30 Year FRM
Assume Prepays in 5 years:
N=60
I=9/12
pmt=733.76
FV=95,069.26
PV=???96,068
The lender needs to charge 3,932 in fees
Assume Prepays in 10 years
N=120
I=9/12
pmt=733.76
FV=87,724.16
PV=???=93,710
The lender needs to charge 6,290 in fees