Section 3.5. The Mathematics of Finance - Loans. Homework

Section 3.5: The Mathematics of Finance - Loans Homework #1-6: 1) A new car is purchased and a $20,000 loan is taken. The loan is for 5 years (60 months) and the interest rate is 7.9% compounded monthly. What is the monthly payment? 2) A new car is purchased and a $30,000 loan is taken. The loan is for 7 years (84 months) and the interest rate is 2.9% compounded monthly. What is the monthly payment? 3) A used car is purchased and a $15,000 loan is taken. The loan is for 4 years (48 months) and the interest rate is 5.9% compounded monthly. What is the monthly payment? 4) A used car is purchased and a $10,000 loan is taken. The loan is for 3 years (36 months) and the interest rate is 8% compounded monthly. What is the monthly payment? 5) $150,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 4.5% compounded monthly. What is the monthly payment? (We are ignoring property taxes and insurance.) 6) $200,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 4.5% compounded monthly. What is the monthly payment? (We are ignoring property taxes and insurance.) Homework #7-12: 7) A new car is purchased and a $20,000 loan is taken. The loan is for 5 years (60 months) and the interest rate is 7.9% compounded monthly. What is the balance after 3 years? 8) A new car is purchased and a $30,000 loan is taken. The loan is for 7 years (84 months) and the interest rate is 2.9% compounded monthly. What is the balance after 3 years? 9) A used car is purchased and a $15,000 loan is taken. The loan is for 4 years (48 months) and the interest rate is 5.9% compounded monthly. What is the balance after 1 year? 10) A used car is purchased and a $10,000 loan is taken. The loan is for 3 years (36 months) and the interest rate is 8% compounded monthly. What is the balance after 1 year? 11) $150,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 4.5% compounded monthly. What is the balance after 15 years? 12) $200,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 4.5% compounded monthly. What is the balance after 10 years? Homework #13-18: 13) A new car is purchased and a $30,000 loan is taken. The loan is for 6 years (72 months) and the interest rate is 5.9% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? 14) A new car is purchased and a $20,000 loan is taken. The loan is for 7 years (84 months) and the interest rate is 6% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? 15) A used car is purchased and a $10,000 loan is taken. The loan is for 3 years (36 months) and the interest rate is 6% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? 16) A used car is purchased and a $18,000 loan is taken. The loan is for 5 years (60 months) and the interest rate is 9% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? 17) $200,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 4% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? 18) $250,000 is borrowed for the purchase of a new home. The loan is for 30 years (360 payments) and the interest rate is 5.25% compounded monthly. a) What is the monthly payment? b) How much interest will be paid over the term of the loan? Homework: 19 - 24 19) $10,000 is still owed on a car loan. The loan has an interest rate of 2.9% compounded monthly and calls for monthly payments. The current payment is $200 per month. How long will it take to pay the loan off? Round to the nearest month. 20) $25,000 is still owed on a car loan. The loan has an interest rate of 7.9% compounded monthly and calls for monthly payments. The current payment is $450 per month. How long will it take to pay the loan off? Round to the nearest month. 21) $15,500 is still owed on a car loan. The loan has an interest rate of 6% compounded monthly and calls for monthly payments. The current payment is $300 per month. How long will it take to pay the loan off? Round to the nearest month. 22) $8,500 is still owed on a car loan. The loan has an interest rate of 4% compounded monthly and calls for monthly payments. The current payment is $250 per month. How long will it take to pay the loan off? Round to the nearest month. 23) $150,000 is still owed on a home loan. The loan has an interest rate of 4.5% compounded monthly and calls for monthly payments. The current payment is $1,100 per month. How long will it take to pay the loan off? Round to the nearest month. 24) $200,000 is still owed on a home loan. The loan has an interest rate of 6.25% compounded monthly and calls for monthly payments. The current payment is $1200 per month. How long will it take to pay the loan off? Round to the nearest month. Homework: 25 – 31 25) Anthony can afford $250 per month for a truck payment. What size of a truck loan can he take if he plans to finance at: a) 6 years (72 months) at an interest rate of 6% compounded monthly? b) 5 years (60 months) years at an interest rate of 6% compounded monthly? 26) Sarah can afford $400 per month for a car payment. What size of a car loan can she take if he plans to finance at: a) 6 years (72 months) at an interest rate of 2.9% compounded monthly? b) 7 years (84 months) years at an interest rate of 2.9% compounded monthly? 27) Kris can afford $475 per month for a car payment. What size of a car loan can she take if he plans to finance at: a) 6 years (72 months) at an interest rate of 6% compounded monthly? b) 7 years (84 months) years at an interest rate of 6% compounded monthly? 28) Lisa can afford $300 per month for a truck payment. What size of a truck loan can she take if he plans to finance at: a) 6 years (72 months) at an interest rate of 2.9% compounded monthly? b) 7 years (84 months) years at an interest rate of 2.9% compounded monthly? 29) Jack and Jill can afford $1200 per month for a house payment. What size of a home loan can the take if they plan to finance for 30 years (360 months) at 4.5% compounded monthly? (This ignores property taxes and insurance that will likely be part of the house payment. I don’t want to over-complicate this problem.) 30) Herman and Lilly can afford $900 per month for a house payment. What size of a home loan can the take if they plan to finance for 30 years (360 months) at 4.25% compounded monthly? 31) Jethro and Ellie can afford $750 per month for a house payment. What size of a home loan can the take if they plan to finance for 30 years (360 months) at 5.25% compounded monthly? Answers 1) Answer: $404.57 N I PV PMT FV P/Y C/Y 60 7.9 20000 solve 0 12 12 Begin / End End 3) Answer: $351.59 N I PV PMT FV P/Y C/Y 48 5.9 15000 solve 0 12 12 Begin / End End 5) Answer: $760.03 N I PV PMT FV P/Y C/Y 360 4.5 150000 solve 0 12 12 7) Make sure your TVM solve looks like problem 1. BAL(36) Answer: $8954.32 9) Make sure your TVM solve looks like problem 3. BAL(12) Answer: $11,574.29 11) Make sure your TVM solve looks like problem 5. BAL(180) Answer: $99,350.93 Begin / End End 13a) Answer: $495.77 N I PV PMT FV P/Y C/Y 72 5.9 30000 solve 0 12 12 Begin / End End 13b) ∑ 𝐼𝑛𝑡( 1,72) Answer: $5695.56 15a) Answer: $304.22 N I PV PMT FV P/Y C/Y 36 6 10000 solve 0 12 12 Begin / End End 15b) ∑ 𝐼𝑛𝑡( 1,36) Answer: $951.90 17a) Answer: $954.83 N I PV PMT FV P/Y C/Y 360 4 200000 solve 0 12 12 Begin / End End 17b) ∑ 𝐼𝑛𝑡( 1,360) Answer: $143,739.01 19) Answer: (53.36 months) 53 full payments and one partial payment N I PV PMT FV P/Y C/Y Solve 2.9 10000 -200 0 12 12 Begin / End End 21) Answer: (59.92 months) 59 full payments and one partial payment N I PV PMT FV P/Y C/Y Solve 6 15500 -300 0 12 12 Begin / End End 23) Answer: 191.33 payments (191 full payments and one partial payment) 191 months is 15 years and 11 months. N I PV PMT FV P/Y C/Y Solve 4.5 150000 -1100 0 12 12 Begin / End End 25a) Answer: $15,084.88 N I PV PMT FV P/Y C/Y 72 6 solve -250 0 12 12 Begin / End End 25b) Answer: $12,931.39 N I PV PMT FV P/Y C/Y 60 6 solve -250 0 12 12 Begin / End End 27a) Answer: $28,661.27 N I PV PMT FV P/Y C/Y 72 6 solve -475 0 12 12 Begin / End End 27b) Answer: $32,515.20 N I PV PMT FV P/Y C/Y 84 6 solve -475 0 12 12 Begin / End End 29) Answer: $236,833.39 N I PV PMT FV P/Y C/Y 360 4.5 solve -1200 0 12 12 Begin / End End 31) Answer: $135,819.44 N I PV PMT FV P/Y C/Y 360 5.25 solve -750 0 12 12 Begin / End End