ONLY CERTAIN PROBLEMS HAVE SOLUTIONS. THE REMAINING WILL BE ADDED OVER TIME. 1. Kathy can take out a loan of 50,000 with Bank A or Bank B. With Bank A, she must repay the loan with 60 monthly payments using the amortization method with interest at 7% compounded monthly. With Bank B, she can repay the loan with 60 monthly payments using the sinking fund method. The sinking fund will earn 6.5% compounded monthly. What interest rate can Bank B charge on the loan so that Kathy s payment will be the same under either option? a. 6.56% compounded monthly b. 6.78% compounded monthly c. 7.00% compounded monthly d. 7.25% compounded monthly e. 7.47% compounded monthly 2. A loan of 0,000 is being repaid with annual payments at the end of each year for years. The interest rate on the loan is.25%. Each annual payment increases by 5% over the previous annual payment. Calculate the principal in the fifth payment. a. 5,533 b. 6,850 c. 8,339 d.,020 e. 11,915 3. A loan of 30,000 is to be repaid using the sinking fund method over 6 years. The interest on the loan is paid at the end of each year and the interest rate is %. The sinking fund payment is made at the beginning of each year with the sinking fund earning 6%. Calculate the amount paid into the sinking fund each year. a. 3535 b. 3828 c. 3888 d. 4057 e. 4301
4. (S08T2) A loan is being repaid with annual payments for 20 years. The principal in the 5 th payment is $4236.99. The principal in the payment is $5670.05. Calculate the amount of the loan to the nearest dollar. a. 80,147.84 b. 83,396.31 c. 116,467.79 d. 123,456 e. 215,268.80 We know: 20 1 11 n=20, 4236.99, and 20 5 1 16 5670.05 Using the given information we can find i 16 Q 4236.99v Substitute for Q in the other given equation 16 11 4236.99v v 5670.05 v 5 1.338225958 5 1i 1.338225958 i.06 Now we can find Q by plugging i=.06 into either given equation Q 4236.99 1.06 16 763.44468 The total loan = Qa so, 20 1 1.06 20 Qa 763.44468 123456 20.06
5. (S09T2) A 30 year mortgage is being repaid with level monthly payments. The principal in the 30 th payment is 90.43. The principal in the 60 th payment is 6.61. Calculate the interest in the 90 th payment. a. 24.42 b. 427.22 c. 429.57 d. 430.26 e. 434.54 We know: n=30(12)=360, 360 60 1 301 90.43, and 360 30 1 331 6.61 We need to use the given information to find i 331 Q 90.43v Substitute for Q in the other given equation 331 301 90.43v v 6.61 v 30 1.178922924 30 1i 1.178922924 i.005501788 Now we can find Q 331 Q 1.005501788 90.43 Q 555.9489515 Now we can calculate the interest in the 90 th payment (360901) 555.9489515 1 1.005501788 430.26
6. (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 annual payments. The annual effective interest rate on the loan is %. 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 years will exactly repay the loan. Fang Finance Company offers an amortization loan with level annual payments at an annual effective interest rate of i. The total annual payments are the same under either loan. Calculate i. a. 5.86% b. 6.29% c. 11.124% d. 20.88% e. 21.34% First, find the payment: L 200, 000 D I il 0.1(200, 000) 34,137.18549 s 1.075 1 n.075 Then use your calculator to solve for i: PV=-200,000; N=; PMT= 34,137.18549; CPT I/Y=11.12%
7. (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 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? a. 4.13% b. 5.54% c. 5.96% d. 7.322% e. 7.95% 500, 000 Payment I D i(500, 000) i(500, 000) 39,572.287 1.05 1.05 Payment * a 500, 000 500, 000 Payment 69,552.345 1 1 1.065.065 500, 000i 39,352.287 69,552.345 i 0.0596
8. (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. a. 30.79 b. 328.91 c. 338.78 d. 348.65 e. 513. First we have to find P using the P and Q formula. P = 30P and Q=-P P 0.06 30 30 Pa ( a 30 v ) 50, 000 30 30 P 184.78 Now next we have to find the outstanding loan balance after the 28 th payment which is equal to the present value of future payments. The future payments are 2P at time 29 and P at time 30. Therefore, OLB Pv Pv 2 1 2 28 2 2(184.78)(1.06) 184.78(1.06) 513. The interest in the 29 th payment is ( OLB28)( i) 513.(0.06) 30.79 Then the principal in the 29 th payment is the 29 th payment less the Interest in the 29 th Payment which is 2P Interest 2(184.78) 30.79 338.78