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4-C Section 4C Loan Payments, and Credit Cards Pages 250-264 4-C Loan Basics The principal is the amount of money owed at any particular time. Interest is charged on the loan principal. 4-C Suppose you borrow $1200 at an annual interest rate of APR = 12% Show the balance of the loan if you pay only the interest due for 6 months. Month Prior Interest Payment Total New Principal Principal .12/12 = toward Payment 1% Principal 1 $1200 $12 $0 $12 $1200 2 $1200 $12 $0 $12 $1200 3 $1200 $12 $0 $12 $1200 4 $1200 $12 $0 $12 $1200 5 $1200 $12 $0 $12 $1200 6 $1200 $12 $0 $12 $1200 BAD IDEA 4-C Suppose you borrow $1200 at an annual interest rate of APR = 12% Show the balance of the loan if you pay $200 toward principal, plus interest for 6 months. Month Prior Interest Payment Total New Principal Principal .12/12 = toward Payment 1% Principal 1 $1200 $12 $200 $212 $1000 2 $1000 $10 $200 $210 $800 3 $800 $8 $200 $208 $600 4 $600 $6 $200 $206 $400 5 $400 $4 $200 $204 $200 6 $200 $2 $200 $202 $0 VARYING PAYMENT AMOUNTS 4-C Suppose you borrow $1200 at an annual interest rate of APR = 12% Show the balance of the loan if you pay $200 for 6 months. INSTALLMENT LOAN Month Prior Interest Payment Total New Principal Principal 1% toward Payment Principal 1 $1200 $12 $188 $200 $1012 2 $1012 $10.12 $189.88 $200 $822.12 3 $822.12 $8.22 $191.78 $200 $630.34 4 $630.34 $6.30 $193.70 $200 $436.64 5 $436.64 $4.37 $194.63 $200 $242.01 6 $242.01 $2.42 $197.58 $200 $44.43 decreasing increasing 4-C Loan Basics The principal is the amount of money owed at any particular time. Interest is charged on the loan principal. To pay off a loan, you must gradually pay down the principal. Each payment should include all the interest plus some amount that goes toward paying off the principal. 4-C Suppose you want to pay off a loan with regular (equal) monthly payments in a certain amount of time. Use Loan Payment Formula (pg 252) APR P PMT = n (nY ) APR 1 1 + n PMT = equal regular payment P = starting loan principal (amount borrowed) APR = annual percentage rate (as a decimal) n = number of payment periods per year Y = loan term in years 4-C Suppose you borrow $1200 at an annual interest rate of APR = 12% How much should you pay each month in order to pay off the loan in 6 months. APR P PMT = n (nY ) APR 1 1 + n .12 1200 PMT = 12 (12 0.5) .12 1 1 + 12 CALCULATOR 4-C 1200 .01 PMT = 1 1 + .01 ( 6 ) CALCULATOR PMT = 12 1 .942045235... PMT = 12 .057954765... PMT = $207.06 4-C The Loan Payment Formula (pg 252) can be used for • student loans • fixed rate mortgages • credit card debt • auto loans More Practice . . . 4-C A student loan of $25,000 at a fixed APR of 10% for 20 years a) Determine the monthly payment. b) Determine the total payment over the term of the loan. c) Determine how much of the total payment over the loan term goes to principal and how much to interest. .10 25,000 PMT = 12 (12 20) = $241.26 .10 1 1 + CALCULATOR 12 Total Payment: $241.26 × 12 × 20 = $57,902.40 Principal Payment: $25,000 Interest Payment: $57,902.40 – $25,000 = $32,902.40 4-C A home mortgage of $100,000 with a fixed APR of 8.5% for 30 years. a) Calculate the monthly payment. b) Calculate the portions of the payments that go to principal and to interest during the first 3 months. Use a table. .085 100000 PMT = 12 (1230) = $768.91 .085 1 1 + 12 Month Prior Total Interest Payment New Principal Principal Payment 0.7083% toward Principal 1 $100,000 $768.91 $708.33 $60.58 $99,939.40 2 $99,939.40 $768.91 $707.90 $61.01 $99,878.39 3 $99,878.39 $768.91 $707.47 $61.44 $99,816.95 4-C Suppose you have a credit card balance of $2500. The credit card APR is 18% and you want to pay it off in 1 year. Determine the monthly payment assuming you make no more credit card purchases. .18 2500 PMT = 12 (121) = $229.20 .18 1 1 + 12 Total Payment: $229.20 ×12 = $2750.40 Principal Paid: $2500 Interest Paid: $2750.40 – $2500 = $250.40 4-C You need to borrow $10,000 to buy a car and you determine that you can afford monthly payments of $220. The bank offers three choices: a 3 year loan at 7%, a 4 year loan at 7.5% or a 5 year loan at 8%. Which option is best for you? 4-C You need to borrow $10,000 to buy a car and you determine that you can afford monthly payments of $220. The bank offers three choices: a 3 year loan at 7%, .07 10,000 PMT = 12 = $308.77 (123) .07 1 1 + 12 $308.77 × 12 × 3 = $11,115.79 4-C You need to borrow $10,000 to buy a car and you determine that you can afford monthly payments of $220. The bank offers three choices: a 4 year loan at 7.5% or .075 10,000 PMT = 12 (12 4) = $241.79 .075 1 1 + 12 $241.79 × 12 × 4 = $11,605.90 4-C You need to borrow $10,000 to buy a car and you determine that you can afford monthly payments of $220. The bank offers three choices: a 5 year loan at 8%. .08 10,000 PMT = 12 = $202.76 (125) .08 1 1 + 12 $202.76 × 12 × 5 = $12,165.60 4-C You need to borrow $10,000 to buy a car and you determine that you can afford monthly payments of $220. The bank offers three choices: a 3 year loan at 7%, $308.77 $308.77 × 12 × 3 = $11,115.79 a 4 year loan at 7.5% or $241.79 $241.79 × 12 × 4 = $11,605.90 a 5 year loan at 8%. $202.76 $202.76 × 12 × 5 = $12,165.60 Which option is best for you? 4-C Home Mortgages may be more complicated: • interest rate (lower) • down payment • closing costs •direct fees • points (each point is 1% of the loan amount) 4-C You need a loan of $80,000 to buy a home. In each of the two choices, calculate your monthly payments and total closing costs. Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points. Choice Monthly Closing Closing Total Total Payment Cost Cost Closing Costs (direct) (points) Costs 1 $545.74 2 $518.88 .0675 .0725 80000 80,000 12 12 PMT = PMT = (1230) (1230) .00675 .0725 1 1 + 1 1 + 12 12 4-C You need a loan of $80,000 to buy a home. In each of the two choices, calculate your monthly payments and total closing costs. Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points. Choice Monthly Closing Closing Total Total Payment Cost Cost Closing Costs (direct) (points) Costs 1 $545.74 2 $518.88 .0675 .0725 80000 80,000 12 12 PMT = PMT = (1230) (1230) .00675 .0725 1 1 + 1 1 + 12 12 $545.74 12 30 $196,466.4 $518.88 12 30 $186,796.8 4-C You need a loan of $80,000 to buy a home. In each of the two choices, calculate your monthly payments and total closing costs. Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points. Choice Monthly Closing Closing Total Total Payment Cost Cost Closing Costs (direct) (points) Costs 1 $545.74 $1200 $800 2 $518.88 $1200 $2400 $545.74 12 30 $196,466.4 $518.88 12 30 $186,796.8 $80,000 .01 $800 $80,000 .01 3 $2400 4-C You need a loan of $80,000 to buy a home. In each of the two choices, calculate your monthly payments and total closing costs. Choice 1: 30 year fixed rate at 7.25% with closing costs of $1200 and 1 point. Choice 2: 30 year fixed rate at 6.75% with closing costs of $1200 and 3 points. Choice Monthly Closing Closing Total Total Payment Cost Cost Closing Costs (direct) (points) Costs 1 $545.74 $1200 $800 $2000 196,466 + 2000 = $198,466 2 $518.88 $1200 $2400 $3600 186,797 + 3600 =$190,397 $545.74 12 30 $196,466.4 $518.88 12 30 $186,796.8 $80,000 .01 $800 $80,000 .01 3 $2400 4-C Homework: Pages 265-267 #16, 28, 30, 40, 44, 46