Question 1

To determine the amount to be deposited in a bank today to grow to $5,000 three years from now at 7% which table should be used?
A) Present value of 1.
B) Future value of 1.
C) Present value of an annuity.
D) No table is required, just multiply $5,000 by 1.07.

Accepted Answer

To find the amount to be deposited today (present value) to grow to a future amount, the "Present value of 1" table is used. This table helps calculate how much one needs to invest now to reach a specific amount in the future, considering a certain interest rate over a set period.

Question 2

The future value of an annuity is:
A) Always more than the present value.
B) Always less than the present value.
C) Equal to the present value.
D) Double the present value.

Accepted Answer

The future value of an annuity is always more than the present value because of the time value of money. As time passes, the value of money depreciates due to inflation, and thus the value of the annuity increases.

Question 3

Anthony Driver wants to buy a new car in 4 years. He knows that he can earn 6% interest compounded semi-annually. How much must he deposit now in order to have $26,000 at the end of 4 years?
A) $21,390.20.
B) $20,524.66.
C) $38,413.96.
D) $31.603.26.

Accepted Answer

We can use the formula for future value of a lump sum:

FV = PV(1 + r/n)^(nt)

Where:
FV = future value
PV = present value (what we want to find)
r = annual interest rate (6%)
n = number of times interest is compounded per year (2, since it is compounded semi-annually)
t = number of years (4)

Plugging in the values:
$26,000 = PV(1 + 0.06/2)^(2*4)
$26,000 = PV(1.03)^8
PV = $20,524.66

Therefore, Anthony must deposit $20,524.66 now in order to have $26,000 at the end of 4 years.

Question 4

Financial instruments are recorded at:
A) Future values.
B) Present values plus interest.
C) Present values less interest.
D) Present values.

Accepted Answer

Financial instruments are recorded at their present values, which represents their fair value at the time of initial recognition. This reflects the amount of cash that would be received or paid if the instrument was settled at that moment.

Question 5

A scholarship fund has $75,000 to invest now to provide scholarships to high school students. They want to have at least $150,000 in 8 years. What rate of interest must they invest this money at to reach their goal?
A) 8%.
B) 9%.
C) 10%.
D) 11%.

Accepted Answer

The answer of A scholarship fund has $75,000 to invest...

Question 6

To determine the present value of a single amount to be received or paid at a future time you need to know all of the following except:
A) The interest rate or discount rate.
B) The number of periods.
C) The future value.
D) The time between periods.

Accepted Answer

The time between periods is not necessary to determine the present value of a single amount; what's needed is the interest rate, the number of periods until the payment or receipt, and the future value of the amount.

Question 7

The present value of an investment is:
A) The amount an investor would pay today to receive a certain amount in the future.
B) The amount an investor would pay today plus the interest the investor would expect to receive a certain amount in the future.
C) The amount an investor would pay today less the interest the investor requires.
D) 90% of the future value of an investment.

Accepted Answer

The present value of an investment is the amount an investor would pay today to receive a certain amount in the future. It does not include any interest or discounting.

Question 8

Your wealthy aunt wishes to give you a trip to Paris when you graduate from college in three years. She estimates the trip will cost $4,000. How much must she invest now at 4% to accumulate enough for you to take this trip?
A) $3,287.72.
B) $3,556.00.
C) $4,499.44.
D) $3,161.24.

Accepted Answer

Using the formula for future value of a single sum, we have:

FV = PV(1 + r)^n

Where FV is the future value, PV is the present value, r is the interest rate, and n is the number of compounding periods.

Plugging in the given values:

$4,000 = PV(1 + 0.04)^3

Solving for PV:

PV = $3,556.00 (rounded to two decimal places)

Question 9

Compound interest:
A) Is interest only on the principal amount for several years.
B) Is interest on the principal and previously earned interest.
C) Is interest only on previous interest excluding the principal.
D) Is equal to simple interest received for several years.

Accepted Answer

Compound interest is interest that is earned not only on the principal amount but also on any previously earned interest. This means that the interest earned will increase each year, making the growth rate exponential rather than linear.

Question 10

A note that does not include an interest rate should be recorded at:
A) Its face amount if the difference between face and present value is material.
B) Its present value if the difference between face and present value is material.
C) Its face amount at all times.
D) Its present value at all times.

Accepted Answer

A note that does not include an interest rate should be recorded at its present value if the difference between face and present value is material. This is because without an interest rate, the present value of the note will differ from its face value due to the time value of money. Therefore, the present value should be recorded to accurately reflect the value of the note. If the difference between face and present value is immaterial, then the note can be recorded at its face amount.

Question 11

How much must I invest today in order to have $25,000 in 5 years assuming 12% interest compounded annually?
A) $14,185.75.
B) $15,888.00.
C) $18,681.50.
D) $17.624.00.

Accepted Answer

The answer of How much must I invest today in...

Question 12

If I invest $50,000 today for 5 years and it grows to $84,253, what rate of interest have I received?
A) 5%.
B) 6%.
C) 11%.
D) 12%.

Accepted Answer

We can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where: 
A = final amount (in this case, $84,253)
P = principal (initial investment, $50,000)
r = annual interest rate (what we're trying to find)
n = number of times the interest is compounded per year (we don't know this, so we'll assume it's compounded annually)
t = time (in years)

Plugging in the values we know:

$84,253 = $50,000(1 + r/1)^(1*5)

Simplifying:

1.68506 = (1 + r)^5

Taking the fifth root of both sides:

1 + r = 1.1101

Subtracting 1 from both sides:

r = 0.1101 or 11.01%

Therefore, the answer is C) 11%.

Question 13

Joe Notsosmart invested $10,000 at 8% simple interest for 5 years. How much more would he have received if he had received compound interest annually at the same rate?
A) $4,000.
B) $4,693.
C) $693.
D) $400.

Accepted Answer

The answer of Joe Notsosmart invested $10,000 at 8% simple...

Question 14

The time value of money is based on the idea that:
A) The value of money in the future equals the interest received in the present.
B) The value of money in the future will be greater than an amount available today.
C) The value of money at present over some length of time will be reduced by inflation.
D) The future value of money will become the current value as time passes.

Accepted Answer

The time value of money is based on the idea that the value of money in the future will be greater than an amount available today due to factors such as inflation and investment opportunities. This is why it is important to consider the time value of money when making financial decisions.

Question 15

The present value of a cash amount:
A) Is always less than the future value.
B) Is always more than the future value.
C) Is the same as the future value.
D) Is the same as the actual cash value.

Accepted Answer

The present value of a cash amount is the value of that amount today, taking into account the time value of money. Due to inflation and the potential to earn interest or returns on that amount over time, the present value is almost always less than the future value.

Question 16

If you receive $20,000 as a gift and invest it at 12% compounded quarterly, how much will you have at the end of three years?
A) $32,020.60.
B) $28,515.20.
C) $22,497.20.
D) $14,027.60.

Accepted Answer

Using the formula for compound interest:

A = P(1+r/n)^(n*t)

where:
A = the final amount
P = the principal amount (the initial gift)
r = the annual interest rate (12%)
n = the number of times the interest is compounded per year (4)
t = the time in years (3)

Plugging in the values:

A = 20000(1+0.12/4)^(4*3)
A = 20000(1+0.03)^12
A = 20000(1.03)^12
A = 20000(1.425)
A = $28,500

Therefore, the answer is B).

Question 17

The difference between the present value and the future value of a sum of money depends upon:
A) The rate of interest.
B) The length of time.
C) The rate of interest and the length of time.
D) Neither the rate of interest nor the length of time.

Accepted Answer

The formula for present value and future value takes into account both the rate of interest and the length of time. Therefore, the difference between present and future value depends on both factors.

Question 18

If I invest $100 at the end of each year for four years at 6% how much will I have at the end of the fourth year?
A) $421.24.
B) $437.46.
C) $563.71.
D) $432.95.

Accepted Answer

The answer of If I invest $100 at the end...

Question 19

Judy Bright has just won the lottery. She can elect to receive her winnings in equal payments of $200,000 a year for the next ten years on December 31 or to receive $2,000,000 immediately. If the current interest rate is 6%, which choice will provide the highest amount:
A) Receiving $2,000,000 immediately.
B) Taking equal payments for 10 years.
C) It does not matter since either choice provides the same amount.
D) Refusing to accept the winnings since it is not enough.

Accepted Answer

To determine which option provides the highest amount, we need to calculate the present value of the 10 equal payments and compare it to $2,000,000. Using a present value calculator with a 6% interest rate, the present value of 10 equal payments of $200,000 received at the end of each year is $1,446,276. Meanwhile, receiving $2,000,000 immediately is worth $2,000,000 today. Therefore, receiving the $2,000,000 immediately is the best choice as it provides a higher amount than taking equal payments for 10 years.

Question 20

Financial instruments do not include:
A) Contracts that call for receipts or payment of cash.
B) Equity investment in another business.
C) Cash.
D) Tangible assets.

Accepted Answer

Financial instruments refer to contracts that represent a financial asset of one entity and a financial liability or equity instrument of another entity. Tangible assets are physical assets such as property and equipment, and they are not financial instruments. Therefore, option D is not included in financial instruments.

Quiz 27: The Time Value of Money: Future Amounts and Present Values Answer Key

To determine the amount to be deposited in a bank today to grow to $5,000 three years from now at 7% which table should be used?

The future value of an annuity is:

Anthony Driver wants to buy a new car in 4 years. He knows that he can earn 6% interest compounded semi-annually. How much must he deposit now in order to have $26,000 at the end of 4 years?

Financial instruments are recorded at:

A scholarship fund has $75,000 to invest now to provide scholarships to high school students. They want to have at least $150,000 in 8 years. What rate of interest must they invest this money at to reach their goal?

To determine the present value of a single amount to be received or paid at a future time you need to know all of the following except:

The present value of an investment is:

Your wealthy aunt wishes to give you a trip to Paris when you graduate from college in three years. She estimates the trip will cost $4,000. How much must she invest now at 4% to accumulate enough for you to take this trip?

Compound interest:

A note that does not include an interest rate should be recorded at:

How much must I invest today in order to have $25,000 in 5 years assuming 12% interest compounded annually?

If I invest $50,000 today for 5 years and it grows to $84,253, what rate of interest have I received?

Joe Notsosmart invested $10,000 at 8% simple interest for 5 years. How much more would he have received if he had received compound interest annually at the same rate?

The time value of money is based on the idea that:

The present value of a cash amount:

If you receive $20,000 as a gift and invest it at 12% compounded quarterly, how much will you have at the end of three years?

The difference between the present value and the future value of a sum of money depends upon:

If I invest $100 at the end of each year for four years at 6% how much will I have at the end of the fourth year?

Judy Bright has just won the lottery. She can elect to receive her winnings in equal payments of $200,000 a year for the next ten years on December 31 or to receive $2,000,000 immediately. If the current interest rate is 6%, which choice will provide the highest amount:

Financial instruments do not include: