MAT 450 Assignment: Amortization Problems
1. Construct the amortization schedule for a $20000 debt that is to be amortized in 8
equal quarterly payments at an annual rate of 12 % compounded quarterly on the
unpaid balance.
First, determine the size of the payments, PMT = _________?
Payment #
size of payment
1
2
3
4
5
6
7
8
interest
paid
j = 0.03
$600.00
balance paid unpaid balance
$20000.00
$0.00
How much total interest will be paid over the 8 quarters ?
2. Consider a $100,000 debt that is to be amortized in 360 equal monthly payments
(i.e., 30-year mortgage) at a nominal rate of 6 % compounded monthly on the unpaid
balance. First, determine the size of the payments, PMT = _________?
Construct the first few rows of an amortization schedule
Payment #
1
2
3
4
size of payment
interest paid
balance paid
unpaid balance
$100,000.00
$500.00
And so on…
How much total interest will be paid over the 30 years ?
Determine the outstanding balance after 120 payments using the retrospective approach.
Determine the outstanding balance after 120 payments using the prospective approach.
3. Consider a $100,000 debt that is to be amortized in 250 level payments of principal.
at a nominal rate of 6 % compounded monthly on the unpaid balance. That is, each
payment will equal $400 plus the interest charge for the period. Construct the first few
rows of an amortization schedule
Payment #
1
2
3
4
size of payment
interest paid
balance paid
unpaid balance
$100,000.00
$500.00
And so on…
How much total interest will be paid over the 30 years ?
Determine the outstanding balance after 120 payments.
Problem 3.1.4:
Simply find the present value of the 12 payments 310, 305, 300,…, 255, using j = 0.02.
Problem 3.1.5:
In addition to paying 550 each month, she pays interest on the outstanding balance.
Payment 1, K1 = 550 + 19800(0.01)
Payment 2, K2 = 550 + 19250(0.01)
Payment 3, K3 = 550 + 18700(0.01)
and so on…
Find the present value of the final 20 payments, K17, K18, …, K36.
Problem 3.1.6
In class we find the outstanding balance OB40 using the prospective method. Can you
determine the original amount of the loan and show how to compute OB40 using the
retrospective method?
Problem 3.2.4
By the prospective method, the outstanding balance OBt is the present value of the remaining
payments OBt  Ka60t 0.01 , where the payment size is K  L / a60 0.01 . Thus, the
outstanding balance is given by OBt 
0.5L .
Problem 3.2.7
No hints given. You’re on your own.
La60t 0.01
a60 0.01
. Find t such that the outstanding balance is