Question 1

The concept of compound interest refers to:
A) earning interest on the original investment.
B) payment of interest on previously earned interest.
C) investing for a multiyear period of time.
D) determining the APR of the investment.

Accepted Answer

Compound interest refers to the payment of interest on previously earned interest. As the investment earns interest, the interest is added back to the initial investment, thereby increasing the principal amount. The subsequent interest earned is then calculated based on the increased principal amount, resulting in a compounding effect that leads to a higher return on investment over time.

Question 2

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?
A) $7,472.58
B) $10,303.62
C) $13,000.00
D) $13,382.26

Accepted Answer

FV = PV + (PV × r × t)($10,000) + [($10,000 × .06) × 5] = $13,000.00

Question 3

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?
A) The interest rate is very high.
B) The investment period is very long.
C) The compounding is annually.
D) This is not possible with positive interest rates.

Accepted Answer

It is not possible for a future value calculated with simple interest to exceed a future value calculated with compound interest at the same rate, regardless of the interest rate, investment period or compounding frequency. This is because compound interest takes into account the interest earned on the interest, leading to a greater accumulation over time compared to simple interest.

Question 4

How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now,assuming that the car's current price is $20,000,and inflation will be 4%?
A) $3,774
B) $3,782
C) $3,925
D) $4,080

Accepted Answer

First, we need to calculate the amount of the down payment. A 20% down payment on a $20,000 car is $4,000.

Next, we need to adjust for inflation. In one year, the price of the car will be $20,800 (20,000 x 1.04 = 20,800). So, we need to save up $4,160 (20% of 20,800) for the down payment.

Finally, we can use the formula for present value of a lump sum:
Present Value = Future Value / (1 + r)^n

where r is the annual interest rate and n is the number of periods. In this case, we have one period (one year). Plugging in the values, we get:

Present Value = 4,160 / (1 + 0.06)^1
Present Value = 3,925

Therefore, we need to deposit $3,925 today to accumulate a 20% down payment for the car one year from now.

Question 5

The Excel function for interest rate is RATE (nper,pmt,PV,FV).

Accepted Answer

The RATE function in Excel is used to calculate the interest rate for a loan or investment based on periodic, constant payments and a fixed interest rate. Its syntax is RATE(nper,pmt,PV,FV).

Question 6

In 2002,the U.S.inflation rate was below 2% and a few countries were even experiencing deflation.

Accepted Answer

In 2002, the U.S. inflation rate was indeed below 2% and some countries, such as Japan, were experiencing deflation.

Question 7

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?
A) $88
B) $100
C) $112
D) $200

Accepted Answer

We need to find the principal invested (P) to calculate the interest earned on the investment. Using the formula A = P(1 + r/n)^(nt), where A is the amount after t years, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time period in years, we can rewrite this as:
A = P(1 + 0.12/1)^(1*1)
A = P(1.12)
Since $100 was just credited for interest, A = P + $100. Substituting this into the equation and solving for P:
P + $100 = P(1.12)
$100 = P(0.12)
P = $833.33
Now we can calculate the interest earned in the next year:
I = P(0.12)
I = $833.33(0.12)
I = $100
Therefore, the correct answer is C. $112 is the total amount in the account after the interest is credited, but we are only interested in the interest earned.

Question 8

How much will accumulate in an account with an initial deposit of $100,and which earns 10% interest compounded quarterly for 3 years?
A) $107.69
B) $133.10
C) $134.49
D) $313.84

Accepted Answer

The formula for compound interest is A = P(1+r/n)^(nt), where A is the final amount, P is the principal (initial deposit), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Using this formula, we can calculate the final amount as follows:

A = 100(1+0.10/4)^(4*3)
A = 100(1.025)^12
A = 134.494

Therefore, the final amount that will accumulate in the account is $134.49, which is closest to option C.

Question 9

An annual percentage rate (APR)is determined by annualizing the rate using compound interest.

Accepted Answer

The answer of An annual percentage rate (APR)is determined by...

Question 10

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?
A) $70.00
B) $80.14
C) $105.62
D) $140.00

Accepted Answer

To calculate the interest earned in the third year, we first need to calculate the amount of money accrued at the end of two years. This can be done using the formula A=P(1+r)^n, where P is the principal amount, r is the annual interest rate, and n is the number of years. 
Plugging in the values, we get: A = 1000(1+0.07)^2 = $1,149.69
Now, to calculate the interest earned in the third year, we subtract the amount at the end of two years from the amount at the end of three years. This can be done using the formula I = P(1+r)^n - P(1+r)^(n-1), where I is the interest earned. 
Plugging in the values, we get: I = 1149.69(1+0.07) - 1000(1+0.07)^2 = $80.14. 
Therefore, the best choice is B, as it is the only answer option that matches our calculated result.

Question 11

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?
A) $100.00
B) $105.17
C) $110.50
D) $115.70

Accepted Answer

The formula for continuous compounded interest is A = Pe^(rt), where A is the final amount, P is the principal, e is Euler's number (approximately 2.71828), r is the annual interest rate as a decimal, and t is the time in years. Plugging in the given values, we get A = 1000*e^(0.10*1) = $1,105.17. The interest accumulated during one year is A - P = $1,105.17 - $1,000 = $105.17. Therefore, the best choice is B.

Question 12

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?
A) $130.00
B) $138.83
C) $169.00
D) $353.34

Accepted Answer

Continuous compounding formula is A = Pe^rt, where P is the principal amount, r is the annual interest rate, t is the time in years, and A is the amount after t years. Substituting the given values, we get A = 1000*e^(0.13*1) = $1,138.83. Therefore, the interest earned is $1,138.83 - $1,000 = $138.83. The closest choice to this value is B.

Question 13

What will be the approximate population of the United States,if its current population of 300 million grows at a compound rate of 2% annually for 25 years?
A) 413 million
B) 430 million
C) 488 million
D) 492 million

Accepted Answer

FV = PV(1 + r)^tFV = 300 million × (1.02)²⁵FV = 492.2 million ≈ 492 million

Question 14

Nominal dollars refer to the amount of purchasing power.

Accepted Answer

Nominal dollars refer to the current dollar amount without adjusting for inflation, not directly to purchasing power.

Question 15

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?
A) .4693
B) .5500
C) .6000
D) .6806

Accepted Answer

PV = FV/(1 + r)^tPV = 1/1.08⁵PV = .6806

Question 16

Assume the total expense for your current year in college equals $20,000.Approximately how much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?
A) $952.00
B) $1,600.00
C) $1,728.00
D) $3,973.00

Accepted Answer

The answer of Assume the total expense for your current...

Question 17

Approximately how long must one wait (to the nearest year)for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually?
A) 9 years
B) 14 years
C) 22 years
D) 25 years

Accepted Answer

The answer of Approximately how long must one wait (to...

Question 18

When an investment pays only simple interest,this means:
A) the interest rate is lower than on comparable investments.
B) the future value of the investment will be low.
C) the earned interest is nontaxable to the investor.
D) interest is earned only on the original investment.

Accepted Answer

Simple interest means that interest is earned only on the original investment, rather than on the interest earned. This typically results in a lower future value for the investment compared to compound interest. The interest rate and tax status of the investment are not necessarily affected by whether the interest is simple or compound.

Question 19

The appropriate manner of adjusting for inflationary effects is to discount nominal cash flows with real interest rates.

Accepted Answer

The appropriate manner of adjusting for inflationary effects is to discount real cash flows with real interest rates or to discount nominal cash flows with nominal interest rates.

Question 20

An effective annual rate must be greater than an annual percentage rate.

Accepted Answer

The answer of An effective annual rate must be greater...

Quiz 5: The Time Value of Money

The concept of compound interest refers to:

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?

How much must be deposited today in an account earning 6% annually to accumulate a 20% down payment to use in purchasing a car one year from now,assuming that the car's current price is $20,000,and inflation will be 4%?

The Excel function for interest rate is RATE (nper,pmt,PV,FV).

In 2002,the U.S.inflation rate was below 2% and a few countries were even experiencing deflation.

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?

How much will accumulate in an account with an initial deposit of $100,and which earns 10% interest compounded quarterly for 3 years?

An annual percentage rate (APR)is determined by annualizing the rate using compound interest.

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?

What will be the approximate population of the United States,if its current population of 300 million grows at a compound rate of 2% annually for 25 years?

Nominal dollars refer to the amount of purchasing power.

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?

Assume the total expense for your current year in college equals $20,000.Approximately how much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?

Approximately how long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually?

When an investment pays only simple interest,this means:

The appropriate manner of adjusting for inflationary effects is to discount nominal cash flows with real interest rates.

An effective annual rate must be greater than an annual percentage rate.