Annuities - ch5
Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 13.80%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? a. An investment that matures in eleven years b. An investment that matures in ten years
a. An investment that matures in eleven years
TRUE
After the end of the second year and all other factors remaining equal, a future value based on compound interest will never exceed the future value based on simple interest.
Compound VS Simple Interest Formulas for FV
FV = PV + PV(I*N) ====> Simple FV = PV x (1 + I)^N =====> Compound
Now, assume that Emma's savings institution modifies the terms of her account and agrees to pay 9% in compound interest on her $500 balance. All other things being equal, how much money will Emma have in her account in 11 years?
N=11, I/Y =9% PV = -500 PMT=0 CPT FV FV = 1290.21
2. Simple versus compound interest Emma deposited $500 in a savings account at her bank. Her account will earn an annual simple interest rate of 9%. If she makes no additional deposits or withdrawals, how much money will she have in her account in 11 years?
Solve for Simple Interest PV + PV (R * N) 500 + 500 (.09*11) * DO r*n first (.09*11) = .99 THEN * PV .99 * 500 = 495 THEN add PV 495+500 = 995
Terms CH5
Term Answer Description DiscountingADiscounting is the process of calculating the present value of a cash flow to be received or paid in the future. Compounding, which is the process of determining the future, or terminal, value of a current cash flow, is the opposite of discounting.Time value of moneyDThe financial concept that maintains that the timing of a receipt or payment of a cash flow will affect its value is called the time value of money (TVM). The time value of money illustrates that, due to its capacity to earn interest, a cash flow received today is worth more than an identical cash flow to be received on a future date. The exact current value of a future cash flow is a function of the magnitude of the future cash flow, the return required by the owner (recipient) of the cash flow, and when in the future the cash flow will occur.Amortized loanGAn amortized loan is one that is repaid with payments that are composed of both the interest owed on the loan and a portion of the loan's principal. In contrast, a zero-interest loan is one on which interest is not charged and the payments made to repay the loan will consist only of principal.Ordinary annuityCA series of equal cash flows that are paid or received at regular intervals, such as a day or a month, is called an annuity. When the cash flows occur at the end of each of the regular intervals, the series is called an ordinary annuity. An example of an ordinary annuity is the 60 monthly payments of $676.65 made at the end of each month to repay a $35,000 loan that charges 6% interest and is to be repaid over five years. If the cash flow were to occur at the beginning of each of the regular intervals, then the annuity would be called an annuity due.Annual percentage rateJThe annual percentage rate (APR) is the cost of borrowed funds as quoted by lenders and paid by borrowers, in which the interest required is expressed as a percentage of the principal borrowed. This rate does not reflect the effects of compounding if interest is earned more than once per year.Annuity dueHAn annuity due is the name given to a series of equal cash flows that occur at the beginning of each of the equally spaced intervals (such as daily, monthly, annually, and so on).PerpetuityBA perpetuity is a series of equal cash flows that are expected to continue forever. A perpetuity can be considered to be a special type of annuity. While both a perpetuity and an annuity exhibit constant periodic cash flows, the annuity has a definite end date, and the perpetuity does not. Instead, a perpetuity's cash flows are expected to continue indefinitely.Future valueFA future value represents the amount to which a current (present) value will grow over a given period of time when compounded at a given rate of interest. Mathematically, a future value is calculated as FV = PV x (1 + r)nn.Amortization scheduleEAn amortization schedule or table reports the amount of principal and the amount of interest that make up each payment made to repay a loan by the end of its regular term. Remember, the term amortization has two meanings. One meaning refers to the process of decreasing the principal outstanding on a loan via payments containing both interest and principal. The second meaning refers to the depreciation of the intangible assets owned by a firm.Opportunity cost of fundsIThe interest rate that represents the return on an investor's best available alternative investment of comparable (equal) risk is the investor's opportunity cost of funds.
Formulas
The correct formula for the calculation of the present value of an annuity due is PMT x ({1 - [1/(1 + r)nn]}/r) x (1 + r) where PMT is the amount of the constant cash flow received or paid each period, r is the opportunity cost or the interest rate (return) paid or received each period, and n represents the number of periods for which interest is earned. PMT x ({1 - [1/(1 + r)nn]}/r) is the present value of an ordinary annuity. PMT/r is the equation used to calculate the present value of a perpetuity. PMT x {[(1 + r)nn - 1]/r} x (1 + r) is the formula used to calculate the future value of an annuity due
Eric wants to invest in government securities that promise to pay $1,000 at maturity. The opportunity cost (interest rate) of holding the security is 13.80%. Assuming that both investments have equal risk and Eric's investment time horizon is flexible, which of the following investment options will exhibit the lower price? a. An investment that matures in eleven years b. An investment that matures in ten years
a. An investment that matures in eleven years Because both investments have equal risk and Eric has a flexible time horizon, an investment with a longer maturity will have a lower present value.
Which of the following is true about present value calculations? a. Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases. b. Other things remaining equal, the present value of a future cash flow increases if the investment time period increases.
a. Other things remaining equal, the present value of a future cash flow decreases if the investment time period increases. As the investment time increases, the numerator stays the same, but the denominator increases, leading to a smaller value for PV. A protracted investment time period means that you will have to wait longer to receive the cash flow. The future value gets discounted more and more as the period of discounting increases, thus leading to a lower present value of the cash flow.
Which of the following is true about finding the present value of cash flows? a. Finding the present value of cash flows tells you what a cash flow will be worth in future years at a specified rate of return. b. Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return.
b. Finding the present value of cash flows tells you how much you need to invest today so that it grows to a given future amount at a specified rate of return. Finding the present value of cash flows tells you what cash flows in future years would be worth today. It also tells you how much you need to invest today so that your cash flows grow to a given future amount. The concept of the present value of cash flows is an important part of financial and business decision making.
Which of the following investments that pay will $5,000 in 12 years will have a higher price today? a. The security that earns an interest rate of 8.25%. b. The security that earns an interest rate of 5.50%.
b. The security that earns an interest rate of 5.50%. To find the current value of the investment, calculate the present value of the security that pays $5,000 in 12 years at a given rate of return.
