Your Money and

Your Math

Chapter 13

1

13.4

Buying a House

2

13.4

Step 1. Calculate the minimum cash investment: 3% of price.Step 2. Calculate the FHA down payment:

Acquisition price – FHA loan amount

Down Payment: Higher value between steps 1 and 2Loan amount: Acquisition price – down payment

Down Payment and FHA Loan Amount

3

13.4

1. The Browning family of Colorado (a low closing cost state) want to buy a $77,000 house.

a. If they can get a loan of 80% of the value of the house, what is the amount of the loan?

b. What will be the down payment on this loan?c. If they use an FHA loan, what will be the minimum cash

investment?a. 80% of $77,000 = $61,600

b. $77,000 – $61,600 = $15,400 (20% of $77,000)c. Cash investment is 3% of $77,000 = $2310 (at least)

FHA down payment = Acquisition Price – FHA loan

= $77,000 – (97.65% of $77,000) = $ 77,000 – $75,190.50

= $1809 Down Payment = $2310 (which is their minimum cash investment)

4

13.4

2.Find

a. The minimum cash investment.b. The maximum FHA loan amount.

Sale Price State

$75,000 Jackson, MS

a. Cash investment is 3% of $75,000 = $2250 (at least)

FHA down payment = $75,000 – .9775 x $75,000 = $ 75,000.00 – $73,312.50 = $1687.50

Down Payment = $2250 (minimum cash investment)

b. Loan Amount = $75,000 – $2,250 = $72,7505

13.4

3. Find the total monthly payment, including the taxes and insurance, for the given mortgage loan. (Use Table 13.5 on pp. 922-3)

Time Annual AnnualAmount Rate (Years) Taxes Insurance

$90,000 9% 25 $1200 $960

Table 13.5 yields $8.39

90 x $8.39 = $755.10

Monthly Taxes and Insurance = (1200 + 960) / 12 = $180

Monthly Payment = $755.10 + $180 = $935.10

6

13.4

The monthly payment M for a loan of P dollars for n months at monthly rate i is

Formula to Find the Monthly Payment for a Loan

mt

mr

mr

n

P

i

PiM

11)1(1

7

13.4

4.Assume that the buyer in example 2 is paying closing costs of $700.

a. What is the acquisition cost?b. What is the maximum FHA loan amount?c. Use the formula to find the monthly payment if the loan is at 7½% for 25 years.

a. Acquisition price = $75,000 + $700 = $75,700

b. Loan amount = $75,700.00 – $2387.50 = $73,312.50

251212075.0

12075.0

11

50.73312

mt

m

r

m

rP

M

11

c. $541.77

8

13.4

Minimum cash investment = $75,700 - 0.9775x$75,000 = $2387.50

5.The Bixley family has a $50,000 mortgage loan at 10% for 30 years.

a. What is the family’s monthly mortgage payment?

b. How many payment will the family have to make in all?

c. What is the total amount the family will pay for principal and interest?

d. What is the total interest the family will pay?

9

13.4

$438.79

11

50000 a.

)3012(1210.0

1210.0

M

SOLUTION

b. Number of payments = 12 30 = 360

c. Total Payments = 360 $438.79 = $157,964.40

d. Total Interest = $157,964.40 $50,000.00 = $107,964.4010

13.4

Solution

5. Suppose you purchase a home and obtain a 20-year loan of $225,000 at an annual interest rate of 6.0%. Find the amount of interest that will be paid on the loan over the 20 years.

Example

13.4

.0612

( 12*20).0612

225000$1611.97

1 1

M

$1611.97 12 20 $386,872.80Total Cost

$386,872.80 $225,000 $161,872.80Interest 11

Example6. Joseph has signed a $144,000 mortgage with monthly payments of $1,127.71. The loan is a 30-year fixed-rate mortgage at 8.7%. Determine the unpaid balance after 19 years.

Formula

( 12*( )) ( 12*( ))12

12

1 (1 ) 1 (1 )

t x t xr

r

M i MB

i

B – unpaid balance M – monthly payment i – interest rate per period r – interest rate t – term of mortgage x – elapsed years

Solution

( 12*(30 19)0.08712

0.08712

$1127.71 1 (1 )$95,603.14

B

12

13.4

Amortization ScheduleThe following is the usual headings for an amortization schedule.

Payment Number Payment Interest

per PeriodPortion

to PrincipalPrincipal at

end of Period

Payment zero is the amount of the loan.The periodic payment is found using the formula on slide 7. Interest per Period is found using the formula I = Prt.Portion to Principle is Payment Interest per Period. Interest per Periodmust always be paid first.Principal (Balance) at end of period is Previous Balance Portion to Principal.This balance is the amount needed to pay off the loan early.The last payment is done differently then the rest of the payments. a. Principal at end of Period must be zero. b. Portion to principal is the previous balance. c. Interest per period is calculated as usual. d. The last payment is the sum of the Interest per period and Portion to Principal. This amount is usually different than all of the others because it most zero out the loan.

13

13.4

ExampleEthan has borrowed $3000 at 6% compounded quarterly andhas agreed to pay the loan in quarterly payments over a two year period. Make an amortization schedule for the loan.

Payment Number Payment Interest

per PeriodPortion

to PrincipalPrincipal at

end of Period

0 $3000.00

1

2

3

4

5

6

7

8

13.4

14

Solution

75.400$

11

3000$)2*4(

406.0

406.0

M

Payment Number Payment Interest

per PeriodPortion

to PrincipalPrincipal at

end of Period

0 $3000.00

1 $400.75

2 400.75

3 400.75

4 400.75

5 400.75

6 400.75

7 400.75

8

13.4

Notice the last payment has not been filled in yet.

15

Solution Continued

Payment Number Payment Interest

per PeriodPortion

to PrincipalPrincipal at

end of Period

0 $3000.00

1 $400.75

2 400.75

3 400.75

4 400.75

5 400.75

6 400.75

7 400.75

8

I1 = $3000.00(0.06)() = $45.00

$45.00 $355.75 2644.25

39.66 361.09 2283.16

17.51 383.24 784.64

I2 = $2644.25(0.06)() = $39.66

I3= $2283.16(0.06)() = $34.25

34.25 366.50 1916.66

I4 = $1916.66(0.06)() = $28.75

28.75 372.00 1544.66

23.17 377.58 1167.88

I5= $1544.66(0.06)() = $23.17

11.77 388.98 395.66

I6 = $1167.88(0.06)() = $17.51

I7= $ 784.64(0.06)() = $11.77 I8 = $ 395.66(0.06)() = $ 5.93

401.59 0.00 395.66

13.4

5.93 16END