Your Money and Your Math Chapter 13 13.4 1

Buying a House 13.4 2

Down Payment and FHA Loan Amount 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 2 Loan amount: Acquisition price – down payment 13.4 3

1. The Browning family of Colorado (a low closing cost state) want to buy a $77,000 house. If they can get a loan of 80% of the value of the house, what is the amount of the loan? What will be the down payment on this loan? If they use an FHA loan, what will be the minimum cash investment? a. 80% of $77,000 = $61,600 13.4 b. $77,000 – $61,600 = $15,400 (20% of $77,000) 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

The minimum cash investment. The maximum FHA loan amount. Find The minimum cash investment. The maximum FHA loan amount. Sale Price State $75,000 Jackson, MS 13.4 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 = $72,750 5

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 Annual Amount Rate (Years) Taxes Insurance $90,000 9% 25 $1200 $960 13.4 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

Formula to Find the Monthly Payment for a Loan The monthly payment M for a loan of P dollars for n months at monthly rate i is 13.4 7

Assume that the buyer in example 2 is paying closing costs of $700. What is the acquisition cost? What is the maximum FHA loan amount? Use the formula to find the monthly payment if the loan is at 7½% for 25 years. 13.4 a. Acquisition price = $75,000 + $700 = $75,700 Minimum cash investment = $75,700 - 0.9775x$75,000 = $2387.50 b. Loan amount = $75,700.00 – $2387.50 = $73,312.50 $541.77 8

The Bixley family has a $50,000 mortgage loan at 10% for 30 years. What is the family’s monthly mortgage payment? How many payment will the family have to make in all? What is the total amount the family will pay for principal and interest? What is the total interest the family will pay? 13.4 9

SOLUTION b. Number of payments = 12  30 = 360 13.4 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 = $107,964.40 10

Example 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. Solution 13.4 11

Example Formula Solution 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 13.4 B – unpaid balance M – monthly payment i – interest rate per period r – interest rate t – term of mortgage x – elapsed years Solution 12

Amortization Schedule The following is the usual headings for an amortization schedule. Payment Number Interest per Period Portion to Principal Principal 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 Period must 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. 13.4 13

Example Ethan has borrowed $3000 at 6% compounded quarterly and has agreed to pay the loan in quarterly payments over a two year period. Make an amortization schedule for the loan. Payment Number Interest per Period Portion to Principal Principal at end of Period $3000.00 1 2 3 4 5 6 7 8 13.4 14

Solution Notice the last payment has not been filled in yet. 13.4 Number Interest per Period Portion to Principal Principal at end of Period $3000.00 1 $400.75 2 400.75 3 4 5 6 7 8 13.4 15

Solution Continued I1 = $3000.00(0.06)() = $45.00 Payment Number Interest per Period Portion to Principal Principal at end of Period $3000.00 1 $400.75 2 400.75 3 4 5 6 7 8 13.4 $45.00 $355.75 2644.25 39.66 361.09 2283.16 34.25 366.50 1916.66 28.75 372.00 1544.66 23.17 377.58 1167.88 17.51 383.24 784.64 11.77 388.98 395.66 5.93 395.66 401.59 0.00 16 END