Math 373 Fall 2014 Homework Chapter 5

Transcription

1 Math 373 Fall 2014 Homework Chapter 5 Chapter 5 Section 2 1. (S12HW) Kwaku borrows 100,000 to be repaid with five annual payments. The annual effective interest rate on the loan is 6%. Complete an amortization table for this loan. First we need to find the appropriate payments using our calculator: N 5 I / Y 6 PV 100, 000 CPT PMT 23, Now we can create the Amortization table. Time Payment Interest in Pmt Principal in Payment 2. (S12HW) Syaza has a loan of 15,000 which is being repaid with ten level annual payments of a. Calculate the amount that Syaza will pay in principal over the life of the loan. OLB 0 100, , , , , , , , , , , , , , , , , , , , Total Amount of Principal=Total Loan Amount= 15,000 b. Calculate the amount of interest that Syaza will pay. Interest Paid=Total Amount Paid-Total Loan Amount 10* , 000 5, 000

2 3. (S08T2) Josh has repaid a loan with 4 annual payments of 950 each. The total interest repaid in those four payments was 800. Calculate the annual effective interest rate on the loan. Total Amount Paid=Total Amount of Interest Paid+Total Loan Amount Total Loan Amount 950* Now we can find the interest rate using our financial calculator. PV 3000 N 4 PMT 950 CPT I / Y (S12HW) Cale borrowed money to buy a new car. Payments are made monthly. The loan has an nominal rate of interest of 12% compounded monthly. Immediately after the 15 th payment, Cale has an outstanding loan balance of Calculate the amount of interest in the his 16 th payment. (12) i Amount of interest in the 16 th payment= OLB * (S12HW) Daniel took a loan to buy a new couch for his apartment. He is making monthly payments and the loan has a nominal interest rate of 9% compounded monthly. Immediately after the 8 th payment, Daniel still owes 800 on his loan. The principal in his 9 th payment is 90. Determine the amount of the 9 th payment. (12) i OLB8 800 Princ 9 =90 Payment9=(Principal in Payment 9)+(Interest in Payment 9)= (0.0075) 96

3 6. (S12HW) Connor has a mortgage that is being repaid with monthly payments. The annual effective interest rate on his loan is 8%. The principal in the 120 th payment is 890. Calculate the principal in the 40 th payment. n k 1 To calculate the principle in the kth year use the formula Qv. 12 (12) (12) i i We know that Principle in the 120 th n 121 payment: Qv 890 Principle in the 40 th payment: Qv n41 x We need to solve for x using substitution. First Equation: ( n121) Q Q ( n121) Substitute the Q above for the Q in Qv n41 x. ( n121) n n ( 121) ( 41)

4 7. (S12HW) Alice is repaying a loan with level annual payments of The interest rate on the loan is 7%. The interest in the 2 nd payment is Calculate the interest in the 7 th payment. We know Q 1000 and i n k 1 We can find n using the formula for the kth payment. Q1 v ( n21) n ln( ) 1n ln(1.07) n 13 1n. Now we can find the interest in the 7 th n k 1 payment using Q1 v (1271)

5 8. (S12HW) Taylor has a loan which has an outstanding loan balance of 34,000 immediately after the 9 th payment. The monthly payments of 1000 are level. The interest rate on the loan is a nominal rate of 12%. Calculate Taylor s outstanding loan balance immediately after the 11 th payment. We know Q 1000, First we need to find n a n ln(0.66) 9 n ln(1.01) n ( n9) 9n OLB a n, and 9 Now we can find the OLB after the 11 th payment. ( ) OLB (12) i

6 9. (S08T2) A loan is being repaid with annual payments for 20 years. The principal in the 5 th payment is $ The principal in the 10 payment is $ Calculate the amount of the loan to the nearest dollar. We know n 20, Qv Qv , and Qv Qv First, we need to find i. Q v. Using substitution: v v v (1 i) 5 5 i 0.06 Now we can find Q. 16 Q (1.06) However, we are asked for the total amount of the loan, Qa. 20 Qa

7 10. (S09T2) A 30 year mortgage is being repaid with level monthly payments. The principal in the 30 th payment is The principal in the 60 th payment is Calculate the interest in the 90 th payment. We know, n 30(12) 360, Qv Qv 90.43, and Qv Qv First, we need to find i. Q 90.43v v v v (1 i) i Now we can find Q. Q 331 ( ) Q We are asked to calculate the interest in the 90 th payment: (360901) ( )

8 Chapter 5, Section (S12HW) Chen Corporation borrows 100,000. The loan will be repaid with annual payments for ten years using the sinking fund method. The loan has an annual effective interest rate of 9%. The sinking fund earns an annual effective interest rate of 6%. The payments to the sinking fund will result in the sinking fund being exactly equal to the loan at the end of ten years. a. Calculate the amount of interest that will be paid to the bank each year. I il 0.09(100000) 9000 b. Calculate the sinking fund deposit each year. L D s c. Calculate the amount that will be in the sinking fund immediately after the 4 th payment SF4 Ds ,

9 12. (S12HW) Cui Corporation wants to borrow 200,000. Cui has the choice of the following two loans: Bolle Bank offers a sinking fund loan with 10 annual payments. The annual effective interest rate on the loan is 10%. The annual effective interest rate to be earned by the sinking fund will be 7.5%. The amount in the sinking fund at the end of 10 years will exactly repay the loan. Fang Finance Company offers an amortization loan with 10 level annual payments at an annual effective interest rate of i. The total annual payments are the same under either loan. Calculate i. First, find the payment: L 200, 000 D I il 0.1(200, 000) 34, s n.075 Then use your calculator to find i. PV N 10 PMT 34, CPT I / Y 11.12

10 13. (S08T2) Wozny-Wiggins Corporation wants to borrow 500,000 to be repaid with annual payments over ten years. Dummitt Bank offers a loan using the sinking fund method. The interest rate on the loan is i and the sinking fund will earn 5%. Each year, Wozny-Wiggins must pay the interest on the loan and make a payment into the sinking fund. The payments into the sinking fund are such that the amount in the sinking fund after 10 years will exactly repay the loan. Lumley Bank offers a loan based on the amortization method and an annual effective interest rate of 6.5%. The amount of the payment under this loan is exactly equal to the sum of the interest payment and sinking fund deposit on the loan from Dummitt Bank. Calculate i, the annual effective interest rate on the loan from Dummitt Bank? 500, 000 Payment I D i(500, 000) i(500, 000) 39, Payment * a 500, , 000 Payment 69, , 000i 39, , i

11 Chapter 5, Section (S08T2) A four year loan is being repaid with annual payments. The first payment is The second payment is The third payment is The final payment is The annual effective interest rate is 10%. Create an amortization table for this loan Loan 3000v 4000v 5000v 6000v Time Payment Interest Principal OLB (S09T2) A loan of 50,000 is being repaid with 30 annual payments. The annual effective interest rate on the loan is 6%. The first payment on the loan is 30P. Each subsequent payment decreases by P. Therefore, the second payment is 29P. The third payment is 28P, etc. Calculate the principal in the 29 th payment. First, we need to find P using the P and Q formula where P 30P. QP Note that there are two different P s which is pretty confusing. But we only need to know what we are going to plug into the formula. P Pa 30 50, a v 30 1 P a a v 0.06 P , Now we can find the OLB after the 28 th payment by finding the present value of future payments. The future payments are 2P at time 29 and P at time 30. OLB Pv Pv (184.78)(1.06) (1.06) The interest in the 29 th payment is ( OLB28)( i) (0.06) Then the principal in the 29 th payment is the 29 th payment less the interest in the 29 th payment: 2P Interest 2(184.78)

12 Answers 1. Not Given. The table is self checking as the last OLB should be zero. 2. a. 15,000 b. 5, % , , * 11. a b c. 33, % % 14. Not Given. The table is self checking as the last OLB should be zero * *Note: You may get slightly different answers due to rounding. This may also be true of other problems.