Ch 4

variable annuities

Annuity contracts in which payments can vary based on performance or other non-constant factors

Real Rate

Real rate = rr = [(1 + rNOM)/(1 + Inflation)] - 1.0 - If you were deciding how much money you could withdraw from your investment account each year, the real rate of return is the correct interest rate to use in your annuity calculation.

Growing annuities

a series of payments growing at a constant rate over a time period. To qualify as a growing annuity, the payment should grow or decline at the same rate each period - adjusted for inflation and thus represented in real terms. Therefore, the key part of a growing annuity analysis is to represent the interest rate, future value, and payment in real terms, and not in nominal terms.

nominal rate

also called the annual percentage rate. The nominal interest rate is the rate that lenders typically quote.

Annuities

defined as a series of equal payments at regular intervals either made, received, or both, for a certain number of periods. ex: In this case, the retirement fund is set up to pay a series of equal payments, which means that the person who invested in this fund will receive a regular cash flow for a certain number of years after he or she retires

effective annual rate

interest actually being earned by the investment. If interest is compounded more than once per year, the effective annual rate is greater than the nominal interest rate, because the investment earns interest on the principal as well as on the interest previously earned

Simple Interest

interest paid on the principal alone FV = PV + (PV x I x N) :This equation does not allow for the earning of interest on previously earned interest.

mortgage

is a home loan in which a home buyer borrows a lump-sum amount at either a fixed or variable interest rate and repays it in monthly instalments over a certain period of time. - Variable-rate mortgages, called adjustable-rate mortgages, typically offer relatively lower rates than fixed-rate mortgages but are riskier because they fluctuate based on macroeconomic factors. When a home buyer makes a mortgage payment, part of the payment pays the interest on the loan, and the rest goes toward repaying the principal amount. The part that actually goes toward the principal amount is calculated as payment made minus interest due.

periodic interest rate

is the interest earned each period, and it is calculated by dividing the nominal interest rate by the number of periods.

Compounding

is the term used to describe the process of computing a future value. It requires knowledge of three of the four time-value-of-money variables: - The present value (PV) of the amount invested• The interest rate (I) that could be earned by invested funds• The duration of the investment (N)

Mortgage payments

loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump-sum amount as a loan in the beginning, and then you make monthly payments to the lender.

ordinary annuity

made at the end of each period - Ordinary annuities can be compared to a monthly paycheque because you work for the full month and then receive your paycheque for that month

uneven cash flows

series of cash flows may not always necessarily be an annuity. Cash flows can also be uneven and variable in amount, but the concept of the time value of money will continue to apply

perpetuity

series of payments made at fixed intervals that continue infinitely and can be thought of as an infinite annuity - A perpetuity is a stream of equal payments that occur at regular and fixed intervals and that are expected to continue forever. A perpetuity's present value is calculated as the sum of the discounted, or present value (PV), of each of its future cash flows. That is: PV OF PERPETUITY: payment per period / interest rate per period A perpetuity's returns may take the form of dividends (in the case of preferred stock) or interest payments (as in the case of perpetual bonds, such as the consol bonds issued by the British government during the last several centuries). Although there are an infinite number of cash flows in perpetuity, the present value of the nearer cash flows contributes greatly to its current value, while the more distant cash flows make a smaller—and ever decreasing—contribution to its current value. Nevertheless, a perpetuity's current, or present, value reflects the sum of its discounted expected future cash flows.

decision to purchase a security

should involve a comparison of the security's current cost and the discounted, or present, value of its expected future cash flows. - Invest in the security if the present value of the security's expected future cash flows is greater than or equal to the present value, or current cost, of the security, everything else being equal. Doing so will increase your wealth. Spending more than the security is worth, expressed in discounted terms, will reduce your wealth.

Annuity Due

when a payment is made at the beginning of each period - Annuity due payments are made one period earlier than ordinary annuity payments, so they will earn interest for an additional period. Therefore, the value of an annuity due will be greater than the value of a similar ordinary annuity. - An annuity due always has a higher PV than an ordinary annuity that makes the same periodic payment (PMT) example : Annuity dues can be compared to paying rent on an apartment because you pay your rent for each month at the beginning of the month before you have lived in your apartment for that month.