Chapter 3: Interest Rates and Rates of Return
Why do Lenders [Banks] charge Interest on Loans?
1. Compensation for inflation
2. Compensation for default risk – the chance that the borrower will not pay back the loan
3. Compensation for the opportunity cost of waiting to spend your money
Compounding and Discounting
1. Future Value – the value at some future time of an investment made today
FV = Future Value PV = Present Value P = Principal I = Interest Rate
- Future Value = P x [1 + i] = $1000 x [1 + 0.050] = $1050
- Compound Interest = P x [1 + i] = $1000 x [1 + 0.05] = $1,102.50
2. Present Value – the value today of funds that will be received in the future.
- Discounting: PV = FV / [1 x i] $1000 = $1050 / [1 x 0.05]
1. Present value is sometimes called “present discounted value”
2. The further in the future a payment is to be received, the small its present value
3. The higher the interest rate we use to discount future payments, the smaller the present value
of the payments.
4. The present value of a series of future payments is simply the sum of the discounted value of
each individual payment.
Time Value of Money – Why are funds in the future worth less than funds in the present?
For the same three reasons that lenders charge interest on loans:
1. Dollars in the future will usually buy less than dollars can today
2. Dollars that are promised to be paid in the future may not actually be received.
3. There is an opportunity cost in waiting to receive a payment because you cannot get the
benefits of the goods and services you could have bought if you had the money today
1. Simple Loans
2. Discount Loans
3. Coupon Bonds
1) Face value or par – the amount to be repaid by the bond issuer [the borrower] at maturity.
The face value of the typical coupon bond is $1,000.
2) Coupon – The annual fixed dollar amount of interest paid by the issuer of the bond to the
3) Coupon Rate – The value of the coupon expressed as a percentage of the par value of the
bond. For example, if a bond has an annual coupon of $5 and a face value of $1,000, it’s