Loans
• When we calculate the annual
payment of a loan (A), the
payment is actually composed
of interest and payment on
principal.
• The mechanics are best shown
through an example.
1
Approaches…
Loan problems can be worked
two ways:
1. Create a Table…
2. Work problems in the same
manner we’ve been using…
2
Perspective …
Lender is indifferent between loan
payments and investing loan
amount at interest rate.
Σ Payments = Interest Paid
+(Beginning – Ending Principal)
PW of Loans = PW of Payments
3
Create a Table…
With the following column headings:
•
•
•
•
•
•
Year or payment number
Outstanding principal
Payment
Interest payment
Principal payment
Balance Remaining
(next term’s principal)
4
Problem 1
You borrow $1,000 to help pay for
rent, food, and books. It is to be
repaid in 3 equal, annual payments
starting one year from now. Interest
on the loan is 12% per year,
compounded annually.
Determine the amount of the loan
payments, and the corresponding
principal and interest amounts in each
payment.
5
Problem 2
You wish to payoff the loan at the end
of 2 years after making your second
loan payment.
How much do you owe?
6
Problem 3
A student borrowed $5,000, which she
will repay in 30 equal monthly
installments. After making her 25th
payment, she desires to pay the
remainder of the loan in a single
payment.
At 12% per year, compounded
monthly, what is the amount of the
payment?
7
Problem 4
A company has obtained a $10,000
loan at an interest rate of 12% per
year, compounded annually. The loan
requires $500 payments at the end of
each of the next 3 years (starting one
year from now).
Determine how much must be paid 4
years from now in order to payoff the
loan.
8
Problem 5
If you have an interest-only loan, your
regular payment only covers the interest on
the original principle, and the final payment
covers the rest.
If you had an interest-only loan for $8 000,
determine how much must be paid at the
end of 4 years and at the end of 8 years from
now in order to payoff the loan. Assume 8%
APR, compounded yearly.
What does the cash flow diagram for an
interest-only loan look like? (term)
9