I.
A brief History of Lending
a. Lenders despised throughout history
b. Credit is so basic that we find evidence of loans going back 5,000 years
c. Hard to imagine an economy without it
d. Yet, people still take a dim view of lenders because they charge interest
II.
Introduction
a. Credit is one of the critical mechanisms we have for allocating resources
b. Although interest has historically been unpopular, this comes from the failure to
appreciate the opportunity cost of lending
c. Interest rates
i. Link the present to the future
ii. Tell the future reward for lending today
iii. Tell the cost of borrowing now and repaying later
III.
Valuing Monetary Payments Now and in the Future
a. We must learn to calculate and compare rates on different financial instruments
b. We need a set of tools:
i. Future value
ii. Present value
iii. How and why is the promise to make a payment on one date more or less
valuable than the promise to make it on a different date
IV.
Future Value and Compound Interest
a. Future value is the value on some future date of an investment made today
i. $100 invested today at 5% interest gives $105 in a year. So the future
value of $100 today at 5% interest is $105 one year from now
ii. The $100 yields $5 which is why interest rates are sometimes called a
yield
iii. This is the same as a simple loan of $100 for a year at 5% interest
iv. If the present value is $100 and the interest rate is 5%, then the future
value one year from now is: $100+$100 (0.05)=$105
v. This also shows that the higher the interest ratem the higher the future
value
vi. In general:
1. FV=PV+PV(i)=PV(1+i)
b. The higher the interest rate or the higher the amount invested, the higher the
future value
c. Most financial instruments are not this simple, so what happens when time to
repayment varies
d. When using one-year interest rates to compute the value repaid more than one
year from now, we must consider compound interest
i. The interest on the interest
e. What if you leave your $100 in the bank for two years at 5% yearly interest rate
f.
The future value is:
i. $100+$100(O.05)-$100(0.05)+$5(0.05)+$5(0.05)=$110.25
1. $100(1.05)(1.05)=$100(1.05)
2

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*Sign up*ii. In general
1. FV
n
=PV(1+i)
n
g. Converting n from years to months is easy, but converting the interest rate is
harder
i. If the annual interest rate is 5%, what is the monthly rate?

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