Mortgage Calculation & Amortization: Example Problems

Problem 1: Mortgage Payment Calculation

Sam and Ella are buying their first home. The cost of the house is $360,000. They put 20% down and finance the balance through a 25-year mortgage at i(2) = 4.50%. They have a choice of two mortgages: Mortgage A: Level monthly payments Mortgage B: First monthly payment = $2205.23; Succeeding monthly payments decrease by $5 (a)For mortgage A, how much interest is paid in the 18th payment? How much principal is paid in the 25th payment? What is the total amount of interest paid in the third year of the mortgage?(b)After 3.5 years, Sam and Ella decide to refinance their mortgage at i(2) = 3.25%. But if they do this, they are subject to a penalty equal to three month’s interest on the outstanding balance. What is the size of the new monthly payment under mortgage A? For mortgage B, what would be the size of the next monthly payment (the 43rd payment) if each succeeding payment was to continue to decrease by $5? 2.A loan is $67,000 is being repaid with monthly payments. The interest rate for the first 4 years is i(12) = 7.2% and the monthly payment is $780. After 4 years, the loan is refinanced at i(12) = 5.76% and the monthly payment drops to $730. Then after 3 more years, the loan is refinanced at i(12) = 8.40% and the monthly payment rises to $800. After 9 years, the loan is refinanced at i(12) = 6% and is to be paid off in 2 years, with payments that start at $R and increase by 2% every month. What is the value of R (which is the payment due at the end of the 109th month)? 3.A common payment pattern in an amortized loan involves the borrower making level payments of principal. Consider the following: Ben borrows $12,000 from Jen at i(4) = 4%. Ben repays the loan over 6 years by making 24 equal quarterly payments of principal (12,000/24 = $500). Ben also pays interest on the unpaid balance at the end of each quarter. After 2.5 years (10 payments), Jen sells the rights to future loan payments to Ken. (a)What is the outstanding balance of the loan after 10 payments? (b)If Ken wishes to yield i(4)= 6%, what price should he pay Jen? .The ABC company needs to borrow $3,200,000 and they have narrowed their choices to two loans: •Loan A – i(2) = 6%, amortized over 25-years with semi-annual payments •Loan B – i(2) = 5%, semi-annual payments of interest only are made over 25-years, with the principal repaid in one lump sum at the end of 25-years (a)In order to even consider Loan B, what rate of interest, i(2), must ABC earn on a sinking fund?b)Let’s supposed ABC ended up choosing Loan B and end up being able to earn i(2) = 3% on their sinking fund. After 10-years, senior executives at the company decide to change to the amortization method. At that time the company will pay back the $3,200,000 to the original lender and then finance the rest of the loan (the book value at that time) with a lender who charges i(2) = 4.5%. ABC will payoff the loan over 12 more years with semi-annual payments. What is the total amount of interest ABC ends up paying on the loan over the entire 22 years? Give the answer as the total interest they paid AND also as the total net interest they paid (remember, they had a sinking fund earning them interest for part of the 22 years).

5.A $100,000 bond, redeemable at C, pays n semi-annual coupons at i(2) = 3.5% and is bought to yield i(2) = 4.0%. (a)If the absolute value of the sum of the book value adjustment column for the first 5-years is equal to $1813.49, what is the price of the bond? (b)The book value of the bond after (n ? 2) coupons have been paid is $101,917.53. What is C? 6.Determine the price of the following bonds: (a)A 12-year $5000 bond, redeemable at 101.75, with coupons at i(2) = 5% for the first 6 years and at i(2) = 4.5% thereafter, bought to yield i(2) = 6% for the first 5 years and i(2) = 5.5% thereafterb)An 8-year $2000 bond, redeemable at par, with semi-annual coupons starting at $150 and each succeeding coupon being 90% of the preceding coupon, purchased to yield i(2) = 7%.(c)A 10-year $10,000 par-value bond with semi-annual coupons that starts at $280 and increase by $12 every 6-months thereafter. The desired yield rate is i(2) = 5%. (d)A perpetual bond that pays quarterly coupons of $100, with each succeeding coupon increasing by 0.75% per quarter forever, with a desired yield rat of i(1) = 6%.Computer Questions (use a spreadsheet to solve the following question; don’t forget your name and student number in the right hand header).7.A loan of $50,000 is to be paid back with semi-annual payments over 12 years at i(2) = 9%. The first payment is R and each succeeding payment increases by 8%. Set up an amortization table. Graph the resulting outstanding balances (using a column graph)