XVIII. Amortizations
1.- Consider the construction of an amortization schedule for a $1000 loan repaid in four
annual payments if the annual effective rate of interest is 8%.
2.- A debt of $80,000 is to be amortized with 8 equal semiannual payments. If the interest
rate is 12% compounded semiannually, what is the size of each payment.
3.- A loan of $10,000 is to be amortized with 10 equal quarterly payments. If the interes rate
is 6%, compounded quarterly, what is the periodic payment?
4.- A recent graduate student´s loans total $18,000. If these loans are at 4.2%, compounded
quarterly, for 10 years, what are the quarterly payments?
5.- A homeowner is planning a kitchen remodeling and can afford a $200 monthly payment.
How much can the homeowner borrow for 5 years at 6%, compounded monthly, and still
stay within the budget?
6.- AdriAnne and Anna´s Auto Repair wants to add a new service bay. How much can they
borrow at 5%, compounded quarterly for 4½ years, if the desired quarterly payment is
$6,000?
7.- A $10,000 loan is to be amortized for 10 years with quarterly payments of $334.27. If the
interest rate is 6%, compounded quarterly, what is the unpaid balance immediately after
the sixth payment?
8.- A debt of $8,000 is to be amortized with 8 equal semiannual payments of $1,288.29. If the
interest rate is 12%, compounded semiannually, find the unpaid balance immediately after
the fifth payment.
9.- When Maria Acosta bought a car 2½ years ago, she borrowed $14,000 for 48 months at
8.1% compounded monthly. Her monthly payments are $342.44, but she ´d like to pay off
the loan early. How much will she owe just after her payment at the 2½year mark?
10.- Six and a half years ago, a small business borrowed $50,000 for 10 years at 9%,
compounded semiannually, in order to update some equipment. Now the company would
like to pay off this loan. Find the payoff amount just after the company makes the 14th
semiannual payment of $3,843.81.
11.- A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded
monthly, and if he wants to make monthly payments of $900 for 36 months, how much
must he put down?
12.- A woman buys a car for $40,000. If the interest rate on the loan is 12%, compounded
monthly, and if she wants to make monthly payments of $700 for 3 years, how much must
she have for a down payment?
A woman buys a car for $40,000. If the interest rate on the loan is 12%, compounded
monthly, and if she wants to make monthly payments of $700 for 3 years, how much must
she have for a down payment?
13.- A recent college graduate buys a new car by borrowing $18,000 at 8.4%, compounded
monthly, for 5 years. She decides to pay an extra $15 per payment.
a) What is the monthly payment required by the loan, and how much does she decide to
pay each month
b) How many payments (that include the extra $15) will she make?
c) How much will she save by paying the extra $15?
14.- A young couple buying their first home borrow $85,000 for 30 years at 7.2%, compounded
monthly, and make payments of $576.97. After 3 years, they are able to make a one-time
payment of $2,000 along with their 36th payment.
a) Find the unpaid balance immediately after they pay the extra $2,000 and their 36th
payment.
b) How many regular payments of $576.97 will amortize the unpaid balance from part a)?
c) How much will the couple save over the life of the loan by paying the extra $2,000?
15.- What difference does 0.5% make on a loan? To answer this question, find (to the nearest
dollar) the monthly payment and total interest paid over the life of the loan for each of the
following.
a) An auto loan of $15,000 at 8.0% versus 8.5%, compounded monthly, for 4 years.
b) A mortgage loan of $80,000 at 6.75% versus 7.25%, compounded monthly, for 39 years.
c) In each of these 0.5% differences, what seems to have the greatest effect on the
borrower: amount borrowed, interest rate, or duration of the loan? Explain.
16.- Clark and Lana take a 30-year home mortgage of $121,000 at 7,8%, compounded monthly.
They make their regular monthly payments for 5 years, then decide to pay $1000 per
month.
a) Find their regular monthly payment.
b) Find the unpaid balance when they begin paying the $1000
c) How many payments of $1,000 will it take to pay off the loan?
d) How much interest will they save by paying the loan in this way?
17.- On a credit transaction a debt of $15,000 is pay off with quarter payments of $3,002.68
made during 1.5 years. Calculate the annual rate compounded quarterly.
18.- Elaborate an amortization schedule for a loan of $32,000 for 4 months with an interest
rate of 29%, compounded monthly , if each of the first two payments pays off 30% of the
debt, the third 25% and 15% in the final payment.