Question 1

Compound interest:

Accepted Answer

Compound interest is calculated on the principal amount and the previously earned interest, making it different from simple interest.

Question 2

Financial instruments are recorded at:

Accepted Answer

Financial instruments are recorded at their present value, which is the current value of the future cash flows discounted at a market rate of interest. This method is called the fair value method and is used to accurately reflect the value of the instrument on the balance sheet.

Question 3

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:

Accepted Answer

To compare which choice provides the highest amount, we need to find the present value of the ten-year equal payments option. Using the formula for the present value of an annuity, we get:

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PV is the present value of the annuity, PMT is the equal annual payment, r is the interest rate and n is the number of periods.

Plugging in the values, we get:

PV = $200,000 x [(1 - (1 + 0.06)^-10) / 0.06]
PV = $1,455,930.56

So, the present value of the equal payments option is $1,455,930.56. Since this is less than $2,000,000, the immediate cash option is the best choice.

Question 4

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?

Accepted Answer

The answer of If you receive $20,000 as a gift...

Question 5

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?

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 6

The present value of a cash amount:

Accepted Answer

The present value of a cash amount represents what the cash is worth today, taking into consideration the time value of money (the idea that money today is worth more than the same amount of money in the future due to the potential for investment and earning interest). Therefore, it is always less than the future value, which represents what the cash will be worth in the future without any adjustments for time value.

Question 7

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

Accepted Answer

To find the rate of interest, we can use the formula for compound interest: 
A = P(1 + r/n)^(nt)
where A is the ending amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:
84253 = 50000(1 + r/12)^(12*5)
Dividing both sides by 50,000 and taking the 5th root, we get:
(1 + r/12)^12 = 1.684
1 + r/12 = 1.684^(1/12)
1 + r/12 = 1.11
r/12 = 0.11
r = 0.11 * 12 = 1.32

So the rate of interest is 1.32, which is equivalent to 11%. Therefore, the best choice is C: 11%.

Question 8

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

Accepted Answer

The time value of money is based on the concept that money available today is worth more than the same amount of money in the future due to its potential earning capacity and inflationary factors. Therefore, the value of money in the future will be greater than the value available today.

Question 9

The present value of an investment is:

Accepted Answer

Present value is the discounted value of future cash flows. It represents the amount an investor would pay today to receive a certain amount in the future. It does not include any interest or returns that the investor may expect to receive.

Question 10

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:

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 11

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?

Accepted Answer

Using the formula for future value with simple interest: 
FV = PV(1 + rt), where FV is the future value, PV is the present value, r is the interest rate, and t is the time period.

We know that FV = $4,000, r = 4% or 0.04, and t = 3 years. 
Plugging these values into the formula and solving for PV:

$4,000 = PV(1 + 0.04 x 3) 
$4,000 = PV(1.12) 
PV = $3,556.00

Therefore, your aunt should invest $3,556.00 now at 4% in order for you to have enough money for the Paris trip in three years.

Question 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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

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 the present value represents the true economic cost of borrowing or lending, taking into account the time value of money. Recording the note at its face amount could result in inaccurate financial statements.

Question 15

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?

Accepted Answer

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

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

where:
PV = present value
r = annual interest rate
n = number of times interest is compounded per year
t = time in years
FV = future value

Substituting the given values, we have:

FV = $26,000
r = 6% or 0.06
n = 2 (since interest is compounded semi-annually)
t = 4

So, we need to find PV:

PV = FV / (1 + r/n)^(nt)
PV = $26,000 / (1 + 0.06/2)^(2*4)
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 16

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?

Accepted Answer

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

Question 17

The future value of an annuity is:

Accepted Answer

The future value of an annuity is always more than the present value because of the effect of compounding over time. The interest earned on the annuity each year is added to the principal, resulting in a larger balance at the end of each year.

Question 18

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

Accepted Answer

Both the rate of interest and the length of time impact the calculation of present value and future value. The rate of interest determines the amount of interest earned or paid over time, while the length of time affects how long the interest has to accumulate or the principle has to depreciate. Therefore, the correct choice is C, as both factors are important in determining the difference between present value and future value.

Question 19

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

Accepted Answer

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

Question 20

Financial instruments do not include:

Accepted Answer

Financial instruments are intangible assets that represent a claim to some future cash flow. Tangible assets such as property, plants or equipment are not financial instruments. Therefore, option D is the correct answer.

Quiz 16: The Time Value of Money