Finance 3060 Chapter 5

3 basic types of loans

1. Pure Discount Loans 2. Interes-Only Loans 3. Amortized Loans

There are two ways to calculate future values for multiple cash flows:

1. compound the accumulated balance forward one year at a time 2. calculate the future value of each cash flow first and then add these up

Annuity

A level stream of cash flows for a fixed period of time

Consol

A type of Perpetuity

The present value of a series of futures cash flows is simply the amount that you would need today in order to exactly duplicate those future cash flows (for a given discount rate)

An alternative way of calculating PV for multiple cash flows is to discount back to the present one period at a time

Annuity Due

An annuity for which the cash flows occur at the beginning of the period

Perpetuity

An annuity in which the cash flows continue forever

There can be a huge difference between APR and EAR when interest rates are large.

For example, consider "payday loans." Payday loans are short-term loans made to consumers, often for two weeks or less, and are offered by companies such as Check Into Cash and National Payday. The loans work like this: You write a check today that is postdated (the date on the check is in the future) and give it to the company. They give you some cash. When the check date arrives, you wither go to the store and pay the cash amount of the check, or the company cashed it (or else automatically renews the loan).

If a rate is quoted as 10 % compounded semiannually, then what this means is that the investment actually pays 5 percent every 6 months.

Is 5 percent ever 6 months the same as 10 percent per year? its not. If you invest $1 at 10% per year, you will have $1.10 at the end of the year. If you invest 5 percent every 6 months, then you will have the future value of $1 at 5 percent for two periods or, $1.1025 --the 10 % is called a stated, or quoted, interest rate --the 10.25 %, which is actually the rate you will earn, is called the Effective Annual Rate (EAR)

Is an APR and EAR?

Put another way... If a bank quotes a car loan at 12 percent APR, is the consumer actually paying 12 percent interest? Surprisingly, no. By law, the APR is imply equal to the interest rate per period, multiplied by the number of periods in a year. APR is a quoted, or stated, rate The difference btw APR and EAR won't be all that great as long as the rates are relatively low

Pure Discount Loans

Simplest form of loan The borrower receives money today and repays a single lump sum at some time in the future Very common when the loan term is short

Annual Percentage Rate (APR)

The interest rate charged per period multiplied by the number of periods per year -- this rate must be displayed on a loan document in a prominent and unambiguous way

Effective Annual Rate (EAR)

The interest rate expressed as if it were compounded once per year

Stated Interest Rate

The interest rate expressed in terms of the interest payment made each period. All quoted interest rate.

Amortized Loans

The lender may require the borrower to repay parts of the loan amount over time. The process of paying off a loan by making regular principal reductions is called amortizing the loan A simple way of amortizing a loan is to have the borrower pay the interest each period plus some fixed amount. This approach is common with medium term business loans Probably the most common way of amortizing a loan is to have the borrow make a single, fixed payment every period (ex. car payment)

Interest Only Loan

Type of loan has a repayment plan that calls for the borrower to pay interest each period and to repay the entire principal at some point in the future Notice that if there is just one period, a pure discount loan and an interest only loan are the same thing Most corporate bonds have the general form of an interest only loan

With an ordinary annuity, the cash flows occur at the _____ of each period

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