Chapter 8

What is an annuity?

An annuity is a series of equal cash flows, spaced evenly over time.

What is compound interest? compare to discounting

Compound interest occurs when interest is earned on interest and on the original principal of an investment. Compound interest causes the value of a beginning amount to increase at an increasing rate. Discounting causes the present value of a future amount to decrease at a decreasing rate.

If you are doing PVA and FVA problems, what difference does it make if the annuities are ordinary annuities or annuities due?

In FVA or a PVA of annuity due problems, annuity payments earn interest one period sooner than in ordinary annuity problems. So, higher FVA and PVA values result with an annuity due. The first payment occurs sooner in the case of a future value of an annuity due. In present value of annuity due problems, each annuity payment occurs one period sooner, so the payments are discounted less severely.

Why does money have time value?

Positive interest rates indicate that money has time value. When one person lets another borrow money, the first person requires compensation in exchange for reducing current consumption.

How is present value affected by a change in the discount rate?

Present value is inversely related to the discount rate. If the discount rate increases, present value decreases. If the discount rate decreases, present value increases.

Continuous Compounding

The effect of increasing the number of compounding periods per year is to increase the future value of the investment.

How does continuous compounding benefit an investor?

The more frequently interest is compounded, the greater the future value. The smallest compounding period is used when we do continuous compounding--compounding that occurs every tiny unit of time (the smallest unit of time imaginable)

Time value of money

The time value of money means that money you hold in your hand today is worth more than money you expect to receive in the future. Similarly, money you must pay out today is a greater burden than the same amount paid in the future.

Which formula would you use to solve for the payment required for a car loan if you know the interest rate, length of the loan, and the borrowed amount? Explain.

To solve for k when the known values are PVA, n, and PMT, start with the present value of an annuity formula. . .Then rearrange terms and solve!

Suppose you are planning to make regular contributions in equal payments to an investment fund for your retirement. Which formula would you use to figure out how much your investments will be worth at retirement time, given an assumed rate of return on your investments?

You would use the future value of an annuity formula. This determines the FV of a recurring payment with an assumed ROR