Aim: Money Matters: Home Ownership Course: Math Literacy
Aim: How does money matter? Home ownership – the big Kahuna!
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Aim: Money Matters: Home Ownership Course: Math Literacy
House Buying Terminology
mortgage – the amount that is borrowed to buy real estate. The amount of a mortgage is the difference between the selling price and the down payment.
mortgage = selling price – down payment
down payment – normally between 10% and 30%
closing costs – other expenses associated with purchase of home and are due at when sale of house is finalized (the closing)
loan origination fee – also called points; equal to one percent of mortgage.
Aim: Money Matters: Home Ownership Course: Math Literacy
Model Problem
The purchase price of a home is $98,000. A down payment of 20% is made. The bank charges $450 in fees plus 2½ points. find the total of the down payment and the closing costs.
down payment = 20% of 98,000 = 19,600
mortgage = selling price – down payment = 98,000 – 19,600 = 78,000
points = 2½ % of 78,400 = 1960
Total = 19,000 + 450 + 1960 = $22,010
Aim: Money Matters: Home Ownership Course: Math Literacy
More Terminology
adjustable rate mortgages (ARM) – rate is adjusted periodically to more closely reflect current rates
fixed or conventional mortgages – rate is fixed for the life of loan. Terms of 15, 20, 25, or 30 years are most common.
mortgage payment – the monthly payment
foreclosure – bank takes possession of house due to non-payment of mortgage with right to sell to another buyer
escrow account – part of monthly mortgage payment may go into this account to pay real estate taxes.
Aim: Money Matters: Home Ownership Course: Math Literacy
Buying a House
You purchase a house with a $100,000 loan to be paid off over 30 years in equal monthly installments. The interest rate for the loan is 6%.
a) What is your monthly payment?
b) How much will you eventually pay by the time the loan is ended in 30 years?
c) How much is interest?Amortization – the process of paying off a debt by systematically making partial payments until the principal and interest are repaid.
1 1nt
rPnmrn
Amortization Formula
P – the value of mortgage
Aim: Money Matters: Home Ownership Course: Math Literacy
Buying a House
You purchase a house with a $100,000 loan to be paid off over 30 years in equal monthly installments. The interest rate for the loan is 6%.
a) What is your monthly payment?
b) How much will you eventually pay by the time the loan is ended in 30 years?
c) How much is interest?
1 1nt
rPnmrn
Amortization Formula
12 30
0.0610000012
0.061 112
m
g
r = 0.06P = 100,000
t = 30n = 12$599.55
Aim: Money Matters: Home Ownership Course: Math Literacy
Buying a House
You purchase a house with a $100,000 loan to be paid off over 30 years in equal monthly installments. The interest rate for the loan is 6%.
b) How much will you eventually pay by the time the loan is ended in 30 years?$599.55 12 30 $215,838.19
c) How much is interest?
$215,838.19 100,000 $115,838.19
Aim: Money Matters: Home Ownership Course: Math Literacy
Amortization – Principal/Interest Breakdown
How much principal and interest are paid on the first payment on a loan of $134,000 at 6.5% for 30 years?
1) Find the monthly payment:
1 1nt
rPnmrn
Amortization Formula
12 30
0.06513400012 846.97
0.0651 112
m
g
2) Use simple interest formula for 1st month:I = Prt I = 134,000(0.065)(1/12) 725.83
846.97 725.83 121.14
monthly payment – interest = principal paid
amortization schedules list the breakdown for each month
Aim: Money Matters: Home Ownership Course: Math Literacy
Model Problem
How much interest is saved on a $175,000 30-year fixed rate 7.5% mortgage if the time of the mortgage is reduced to 15 years.
1) Find the monthly payment @ 30 years:
1 1nt
rPnmrn
Amortization Formula
12 30
0.07517500012 1223.625
0.0751 112
m
g
r = 0.075P = 175,000
t = 30n = 12
$1223.625 12 30 $440,505.14
2) Total payments @ 30 years:
3) How much is interest?$440,505.14 175,000 $265,505.14
Aim: Money Matters: Home Ownership Course: Math Literacy
Model Problem
How much interest is saved on a $175,000 30-year fixed rate 7.5% mortgage if the time of the mortgage is reduced to 15 years.
1) Find the monthly payment @ 15 years:
12 15
0.07517500012 1622.272
0.0751 112
m
g
r = 0.075P = 175,000
t = 15n = 12
$1622.272 12 15 $292,008.89 2) Total payments @ 15 years:
3) How much is interest?$292,008.89 175,000 $117,008.89
$265,505.14117,008.89
$148,496.25interest saved
Aim: Money Matters: Home Ownership Course: Math Literacy
Can You Afford It?
You wish to purchase a house for $225,000 with a down payment of $10,000 with a 30-year fixed rate mortgage at 6.48%. Your family income is $59,000. Lenders have guidelines that suggest families can afford to spend about 28% of monthly income on housing to include property taxes and insurance. Can you afford this house?
1) Find the affordable monthly payment:0.28(59,000) / 12 $1376.67
Aim: Money Matters: Home Ownership Course: Math Literacy
Early PayoffA homeowner has a monthly mortgage payment of $645.32 on a 30-year loan at an annual interest rate of 7.2%. After making payments for 5 years, the homeowner decides to sell the house. What is the payoff of the mortgage?
1 1ntr
nP m rn
Present Value of an Annuity Formula
n·t is the remainingnumber of payments
12 250.0721 112645.32 0.072
12
P
g
89,679.01
30 – 5 years = 25 yearsof payments left
Aim: Money Matters: Home Ownership Course: Math Literacy
Can You Afford It?You wish to purchase a house for $225,000 with a down payment of $10,000 with a 30-year fixed rate mortgage at 6.48%. Your family income is $59,000. Lenders have guidelines that suggest families can afford to spend about 28% of monthly income on housing to include property taxes and insurance. Can you afford this house?
2) Find monthly payment based on details of loan.
12 30
0.064821500012 1356.12
0.06481 112
m
g
r = 0.0648P = 215,000
t = 30n = 12
$1376.67what you can afford
With taxes and insurance – not
affordable
Aim: Money Matters: Home Ownership Course: Math Literacy
Equity
Equity – the Amount of principal of a loan that has been repaid
In 1980 a house was purchase for $100,000 with a 30-year mortgage at 8%. After 22 years and 5 months, how much equity did the owner have?
1) Find the monthly payment @ 30 years:
12 30
0.0810000012 $733.76
0.081 112
m
gr = 0.08P = 100,000
t = 30n = 12
Aim: Money Matters: Home Ownership Course: Math Literacy
Equity
In 1980 a house was purchase for $100,000 with a 30-year mortgage at 8%. After 22 years and 5 months, how much equity did the owner have?
910.081 112733.76 $49,940.030.08
12
P
2) Find payoff for 7 years and 7 months of left:360 total payments – 22 x 12 + 5 payments made = 91 payments left
Equity = original loan amount – amount to be paid1 1ntr
nP m rn
Present Value of an Annuity Formula
n·t is the remainingnumber of payments
$100,000 49,940.03$50,059.97