When I wrote this post quite awhile ago the 30year FRM was 3.4 and the 15year FRM was 2.9
The gap between the 30year FRM and 15year FRM is even larger today. Today the rates are 3.6 for the 30year FRM and 2.7 for the 15year FRM.
Homebuyers today should definitely consider the 15year FRM. The first step is to redo the calculations below with current rates.
The gap between the 30year FRM and 15year FRM is even larger today. Today the rates are 3.6 for the 30year FRM and 2.7 for the 15year FRM.
Homebuyers today should definitely consider the 15year FRM. The first step is to redo the calculations below with current rates.
Question One: A person is considering taking out a $180,000
mortgage and must choose between a 15year FRM and a 30year FRM. The interest rate on the 15year mortgage is
2.90 while the interest rate on the 30year mortgage is 3.40.
What are the monthly payments on the two loans?
What are the total interest payments on the two loans over
the life of the loan?
What is the aftertax cost of the interest payments on the
two loans?
What is the tax savings from the tax deductibility of
mortgage interest?
What is remaining loan balance after 15 years for the two
loans?
Answer: The monthly mortgage payment calculation is
directly calculated from the PMT function in Excel. The variables inputted into the PMT function
are the interest rate, the term and the loan balance.
The lifetime interest cost is calculated two ways. The first way involves noting that the
difference between total payments and the repaid loan balance is equal to
interest payments. (180* $1234$180,000)
=$42,193.
The second way involves calculating cumulative interest
payments directly from the CUMIPMT function in Excel. Put Rate=0.029/12, NPER=180, PV=$180,000
STARTPERIOD=1, ENDPERIOD=180, and Type=0 into CUMIPMT and get $42,193.)
The after tax cost of interest payments is (1MTR) x
INTEREST.
The tax savings from interest payments is MTR x INTEREST
The mortgage balance after 15 years is obtained directly
from the FV function in Excel. Note FV (RATE=0.029/12,NPER=180,
PMT=1234,PV180000) is equal to $0.
This is a good way to check your work since the balance on a 15year
mortgage held for 15 years must be $0.
The complete answers are laid out in the table below.
A Comparison of 15year
and 30year FRM


15year FRM

30year FRM

Notes


Rate

0.029

0.034

Assumption

Period

180

360

Assumption

Loan

$180,000

$180,000

Assumption

Payment

$1,234

$798

Calculation From Payment
Function

Interest Cost Calculation
One

$42,193

$107,376

Calculation: Total
Payments  Loan Balance

Interest Cost Calculation
Two

$42,193

$107,376

Calculation From CUMIPT
Function

Marginal Tax Rate

0.3

0.3

Assumption

After Tax Interest Cost

$29,535

$75,163

Calculation:
(1mtr)*Interest Cost

Tax Savings from Mortgage
Deductibility

$12,658.05

$32,212.75

Tax Savings from Mortgage Deduction

Mortgage Balance After
Fifteen Years

$0

$112,435

Calculation: From FV Function

Total Mortgage Payments
Over 15 Years

$222,193

$143,688

Calculation 180*MONTHLY
MORTGAGE PAYMENT

Discussion of Comparison of 15year and 30Year FRM:
·
Over a 15year period the homeowner with the
30year FRM has accumulated $112,435 less house equity than the homeowner with
the 15year FRM.
·
Over the 15year period, the homeowner with the
15year mortgage has paid over $78,000 more in mortgage payments than the
homeowner with the 30year mortgage. However, the owner with the 30year
mortgage is not done yet.
·
The additional tax savings from the use of the
30year FRM is around $20,000.
Other financial math problems can be found here.
Other financial math problems can be found here.
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