FINC 409 Chapter 9: Time Value of Money
The interest portion increases and the principal portion decreases over time under a typical loan amortization schedule. 240
False, decreases, increases
The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year. 243-4
False, for EAR
With compound interest, interest is earned only on the investment's principal.
False, interest is earned only on the investment's principal with simple interest
An annuity due may also be referred to as a deferred annuity. 232
False, not the proper terminology
Level cash flow amounts that occur at the end of each period, starting at the end of the first period, are an annuity due. 232
False, ordinary annuity
An ordinary annuity exists when the equal payments occur at the beginning of each time period. 232
False, ordinary annuity payments occur at the end of each time period
At very high interest rates the "Rule of 72" will result in a small estimation error for the estimate of the time for an investment to double. 232
False, same is true at very low interest rates
Simple interest is interest earned on the investment's principal and subsequently-earned interest. 221
False, simple interest does not earn interest on previously earned interest
If the interest rate is 0% for 10 years, then the present value will be less than the future value. 229
False, the present value will be the same as the future value
The annual percentage rate (APR) overstates the true or effective interest cost. 243
False, understates
The effective annual rate (EAR) is the true opportunity cost measure of the interest rate. 243
True, As compared to the Annual Percentage Rate (APR)
The future value of a $100 ordinary annuity deposited for 10 years at 10% is $1,593.74. 233
True, END mode
The present value of a $100 ordinary annuity deposited for 10 years at 10% is $614.46.
True, END mode
The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $1,593.74 is 10%. 237
True, END mode
The return provided by a $100 ordinary annuity deposited for 10 years that results in a future value of $614.46 is negative 11.45%. 237
True, END mode
The method of calculating the annual percentage rate (APR) is set by law. 243
True, by the Truth in Lending law, APR = r×m, r=interest rate charged per period, m=number of periods, 1%/month → APR=12%
When the annual interest rate stays the same, more frequent interest compounding helps savers earn more interest over the course of the year. 241-2
True, earn interest on the interest sooner → higher FV in future
At very low interest rates, the "Rule of 72" does not approximate the compounding process well. 232
True, same is true at very high interest rates
Compound interest is interest earned on interest in addition to interest earned on the principal. 221
True
Compounding means that interest earned each year, plus the principal, will be reinvested at the stated rate. 221
True
Discounting is an arithmetic process whereby a future sum decreases at a compounding interest rate over time to reach a present value. 225
True
For the same annual percentage rate, more frequent compounding increases the future value of an investor's funds more quickly. 242
True
If the compound inflation rate were greater than the compound interest rate, future purchasing power on our savings would fall. 225
True
Money has a time value so long as interest is earned by saving or investing money. 220-1
True
The Rule of 72 is an estimate of how long it would take to double a sum of money at a given interest rate. 232
True
The effective annual rate (EAR) is sometimes called the annual effective yield. 243
True
The future value of $100 deposited today for years at 10% compounded annually is $259.37. 226
True
The present value of $100 received in 10 years at 10% compounded annually is $38.55. 222
True
The return provided by $100 deposited today for 10 years that results in a future value of $614.46 is 19.91%. 237
True
Your college has agreed to give you a $10,000 tuition loan. As part of the agreement, you must repay $12,600 at the end of the three-year period. What interest rate is the college charging? 230
8%, TVM problem: +10,000, -12,600
Larry deposited $5,000 in a savings account that paid 8% interest compounded quarterly. What is the effective annual rate of interest? 242
8.24% Q14
As the number of periods increases, present value increases. 225-8
False
For a given discount rate, an ordinary annuity and an annuity due have the same present value. 235-6
False
Because interest compounds, the annual percentage rate formula will overstate the true interest cost of a loan. 243
False, APR=rxm ignores interest compounding → it understates the true interest cost
The annual percentage rate is the true opportunity cost measure of the interest rate. 243
False, EAR is a better measure
Which of the following terms best describes an annuity due?
Payment at beginning of year
You need to have $35,000 on hand to buy a new Lexus five years from today. To achieve that goal, you want to know how much you must invest today in a certificate of deposit guaranteed to return you 3% per year. To help determine how much to investment today, you will use: 226
Present value of a simple lump sum, the $35,000 you need 5 years from now is a single lump sum → use present value
A famous athlete is awarded a contract that stipulates equal payments to be made at the end of each month over a period of five years. To determine the value of the contract today, you would need to use: 232
Present value of ordinary annuity
If the stated or nominal interest rate is 10 percent and the inflation rate is 4 percent, the net or differential compounding rate would be ________ percent. 225
Six
$1000 deposited in a bank that earns 7% per year will become approximately $7,600 in 30 years. 221
True
A fixed-rate mortgage is an example of an annuity. 240-1
True
A loan amortization schedule shows the breakdown of each payment between interest and principal, as well as the remaining balance after each payment. 240
True
An amortized loan is repaid in equal payments over a specified time period. 239
True
An annuity is a series of equal payments that occur over a number of time periods. 232
True
As the interest rate increases, present value decreases. 225-8
True
At a zero interest rate, the present value of $1 remains at $1 and is not affected by time. 225-6
True
Select ALL of the following statements that are not descriptive of an amortization schedule? 239-40
a. Each payment is the same. B. The SAME dollar amount of interest is paid with each payment (the dollar amount decreases) c. Payment on principal increases with each total payment. d. Balance owed is reduced by the principal portion of each payment.
Select ALL of the following statements that are false. 243-4
a. For a given APR, more frequent compounding results in additional return on the investment. b. If the number of compounding periods is more than one per year, the APR formula will understate the true or effective interest cost. C. The effective annual rate is determined by multiplying the interest rate charged per period by the number of periods in a year. d. The APR misstates the true interest rate. e. The EAR is the true opportunity cost measure of the interest rate.
Select ALL of the following statements that are true. 226
a. The present value of a future sum decreases as the discount rate increases. b. If the present value of a sum is equal to its future value, the interest rate must be zero. c. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series. *you would need to deposit more today if there are fewer compounding (discounting) periods.
Select ALL of the following variables you would not enter into your financial calculator to calculate the future value five years from today of $2,500 deposited today. 221-22
a. present value (PV) B. future value (FV) c. interest rate (I/Y) D. inflation rate (I) e. number of periods (N) F. payments (PMT)
Select ALL of the following that are variables used in your financial calculator for time value of money calculations for a single lump sum of money. 221-2
a. present value (PV) b. future value (FV) c. interest rate (I/Y) e. number of periods (N)
A series of equal payments or receipts that occur at the beginning of each of a number of time periods is referred to as:
an annuity due
The interest rate determined by multiplying the interest rate charged per period by the number of periods in a year is called the:
annual percentage rate
The method of calculating interest on a loan that is set by law is called the:
annual percentage rate (APR)
In future value or present value problems, unless stated otherwise, cash flows are assumed to be:
at the end of a time period.
When the amount earned on a deposit becomes part of the principal at the end of a period and can earn a return in future periods, this is called:
compound interest.
The interest rate that measures the true interest rate when compounding occurs more frequently than once a year is called the:
effective annual rate
When compounding more than once a year, the true opportunity costs measure of the interest rate is indicated by the:
effective annual rate
The future value of a dollar ________ as the interest rate increases and its future value ________ the farther in the future is the funds are to be received. 224
increases; increases.
The _________ value of a savings or investment is its amount or value at the current time. 220
present
The time value concept/calculation used in amortizing a loan is:
present value of an annuity
Interest earned only on an investment's principal or original amount is referred to as: 221
simple interest
Suppose you have a choice of two equally risky annuities, each paying $1,000 per year for 20 years. One is an annuity due, while the other is an ordinary annuity. Which annuity should you choose? 232
the annuity due, payments are received sooner → worth more today
