Question 1

Compound interest can best be described as:
A) interest on interest only.
B) the discount rate.
C) interest on interest and interest on original principal.
D) interest earned on the original principal.

Accepted Answer

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. This means it includes interest on the original principal and the interest that has been added to that principal.

Question 2

To calculate the present value of an investment the following formula is used: A) 1/(1 + i)ⁿ B) discount rate used in present value cash flow calculations. C) 1/(1 + i)ⁿtimes the future value. D) (1 + i)ⁿ

Accepted Answer

The present value of an investment is calculated by multiplying the future value by the discount factor, which is 1/(1 + i)^n.

Question 3

The future value of an investment is: A) 1/(1 + i)ⁿ B) discount rate used in future value cash flow calculations. C) (1 + i)ⁿtimes the present value. D) (1 + i)ⁿ

Accepted Answer

The future value of an investment is calculated by multiplying the present value by (1 + i)^n, where i is the interest rate and n is the number of periods. This formula is a simplified representation of how the future value grows over time with compound interest, making option C the correct choice.

Question 4

When we consider the time value of money, a dollar received in the future:
A) is worth less than a dollar received today.
B) is worth the same as a dollar received today.
C) is worth more than a dollar received today.
D) depends on the compounding used to determine the relationship to a dollar received today.

Accepted Answer

The time value of money principle states that a dollar received today is worth more than a dollar received in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Question 5

You require an 8% annual return on all investments. You have been offered an investment which will pay you $1,000 in one years time, $2,000 in two years time, and $3,000 in three years time. What is the most you would be willing to pay for this investment?
A) $6,000
B) $2,577
C) $5,022
D) $4,763

Accepted Answer

The answer of You require an 8% annual return on...

Question 6

As a gift from your parents, you have just received $50,000 for your education for the next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the $50,000?
A) $11,096
B) $11,750
C) $12,500
D) $15,096

Accepted Answer

The answer of As a gift from your parents, you...

Question 7

You borrow $95,000 for 12 years at an annual rate of 12%. What are the monthly payments required to amortize this loan?
A) $ 1,248
B) $15,336
C) $ 3,936
D) $11,400

Accepted Answer

To calculate the monthly payment required to amortize a loan, you can use the formula for a fixed-rate loan, which is often represented in financial calculators or spreadsheet functions as PMT(rate, nper, pv), where rate is the monthly interest rate (annual rate divided by 12), nper is the total number of payments (years times 12), and pv is the loan amount (present value). For this loan, the monthly interest rate is 12% / 12 = 1%, or 0.01 as a decimal. The total number of payments is 12 years * 12 months/year = 144 months. Plugging these values into the formula or a financial calculator, you get a monthly payment of approximately $1,248.

Question 8

A perpetuity can be described as:
A) an annuity that lasts longer than 25 years.
B) an annuity that goes on forever.
C) an amount of interest that is annually adjusted and is paid forever.
D) paid until the principal has been repaid.

Accepted Answer

A perpetuity is defined as an annuity that pays out forever, without an end date.

Question 9

How much would you be willing to pay for a preferred share that pays a yearly dividend of $2.80? Current yields on similar preferreds are 6%
A) $46.67
B) $28.00
C) $59.09
D) $29.68

Accepted Answer

The correct answer is A because the preferred share is worth $46.67, which is calculated by dividing the annual dividend of $2.80 by the current yield of 6%.

Question 10

You would like to have $500,000 put away in 20 years for your retirement. You plan to put away $14,000 each year (end of year). What is the minimum interest rate that you would need to receive $500,000?
A) 4.5%
B) 5.72%
C) 6.5%
D) 5%

Accepted Answer

This is a future value of an annuity problem, where you are trying to find the interest rate that will allow a series of equal payments (annuity) to grow to a certain amount in the future. Using the future value of an annuity formula or a financial calculator, you can input the annual payment ($14,000), the number of periods (20 years), and the future value ($500,000) to solve for the interest rate. The correct answer, 5.72%, is the minimum interest rate needed to achieve a future value of $500,000 from annual payments of $14,000 over 20 years.

Question 11

Calculate the present value of $100,000 received in six months. Use an annual discount rate of 10%. Do not adjust the discount rate to a semi-annual rate. Keep it annual and adjust "n" to the appropriate value.
A) $ 56,447
B) $ 90,909
C) $100,000
D) $ 95,346

Accepted Answer

The answer of Calculate the present value of $100,000 received...

Question 12

You would like to retire with $1,000,000. You plan on a 7% annual investment rate (3.5% semi-annually) and will put away $7,500 twice a year at the end of each semi-annual period. How long before you can retire? Round to the nearest figure.
A) 25 years
B) 35 years
C) 51 years
D) 66 years

Accepted Answer

The correct answer is A.The future value of an annuity is given by the formula:FV = P * [(1 + r)^n - 1] / rwhere:P is the amount of each paymentr is the annual interest raten is the number of paymentsIn this case, we have:P = $7,500r = 3.5% semi-annually = 7% annuallyn = ?We want to find the value of n that will give us a future value of $1,000,000. Substituting the given values into the formula, we get:$1,000,000 = $7,500 * [(1 + 0.07)^n - 1] / 0.07Solving for n, we get:n = 50Since we are making payments twice a year, this means that it will take us 50 / 2 = 25 years to retire.

Question 13

If you (1) decrease your required return and (2) decrease the number of compounding periods, what effect would this have on your present value?
A) (1)decrease; (2)increase
B) (1)increase; (2)decrease
C) (1)increase; (2)increase
D) (1)decrease; (2)decrease

Accepted Answer

Decreasing your required return increases the present value because the future cash flows are discounted at a lower rate, making them more valuable today. Decreasing the number of compounding periods also increases the present value because there is less time for the amount to grow, meaning you need less initial investment to reach a future value.

Question 14

What is the future value of an annuity due if your required return is 10%, and payments are $1,000 for 10 years?
A) $11,000
B) $17,531
C) $15,937
D) $16,145

Accepted Answer

The future value of an annuity due can be calculated using the formula: FV = P * [((1 + r)^n - 1) / r] * (1 + r), where P is the payment amount, r is the periodic interest rate, and n is the number of periods. Here, P = $1,000, r = 10% or 0.10, and n = 10. Plugging these values into the formula gives FV = $1,000 * [((1 + 0.10)^10 - 1) / 0.10] * (1 + 0.10) = $17,531 (rounded to the nearest dollar).

Question 15

To calculate the present value of an annuity due you would take the present value of an ordinary annuity answer and 	whereas to calculate the future value of an annuity due you would take the future value of an ordinary annuity answer and 	.
A) divide by (1 + i); multiply by (1 + i)
B) multiply by (1 + i); multiply by (1 + i)
C) multiply by (1 + i); divide by (1 + i)
D) multiply by i; divide by i

Accepted Answer

To calculate the present value of an annuity due, you multiply the present value of an ordinary annuity by (1 + i) because payments are made at the beginning of each period, thus they have one extra period to discount. Similarly, to calculate the future value of an annuity due, you also multiply the future value of an ordinary annuity by (1 + i) because each payment is invested for one additional period compared to an ordinary annuity.

Question 16

To settle a debt you have agreed to make payments of $200, $500, $700, $900, and $1,200 at the end of years 1- 5 respectively. The appropriate discount rate is 8%. What is the present value of your debt?
A) $2,427
B) $3,500
C) $2,100
D) $2,648

Accepted Answer

The present value (PV) of a series of future payments can be calculated by discounting each payment back to the present value using the formula PV = FV / (1 + r)^n, where FV is the future value of the payment, r is the discount rate, and n is the number of periods until the payment is made. For this question, we calculate the present value of each payment individually and then sum them up:1. $200 / (1 + 0.08)^1 = $185.192. $500 / (1 + 0.08)^2 = $427.073. $700 / (1 + 0.08)^3 = $552.314. $900 / (1 + 0.08)^4 = $649.935. $1,200 / (1 + 0.08)^5 = $832.39Adding these amounts together gives us a total present value of $2,647.89, which rounds to $2,648.

Question 17

Four liters of milk cost $3.59 today. How much will it cost you to buy four liters of milk for your grandchildren in 35 years if inflation averages 5% per year?
A) $19.80
B) $12.34
C) $3.77
D) $6.28

Accepted Answer

To calculate the future cost of milk with an average inflation rate of 5% per year for 35 years, you can use the formula for future value: Future Value = Present Value * (1 + inflation rate)^number of years. Plugging in the values: $3.59 * (1 + 0.05)^35 = $19.80.

Question 18

Your parents have promised to give you $25,000 on your wedding day if you wait 10 years to get married. Your sister is getting married today. What amount should she receive in today's dollars to match your gift? The appropriate discount rate is 12%
A) $10,000
B) $22,321
C) $8,049
D) $25,000

Accepted Answer

To match the future value of $25,000 in today's dollars, given a 12% discount rate over 10 years, we use the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($25,000), r is the annual discount rate (12% or 0.12), and n is the number of years (10). Plugging in the values: PV = $25,000 / (1 + 0.12)^10 ≈ $8,049.

Question 19

You want to start saving for retirement. If you deposit $2000 each year at the end of the next 60 years and earn 11% on the investment, how much will you have when you retire?
A) $9,510,132
B) $10,556,246
C) $1,048,114
D) $792,000

Accepted Answer

This is a future value of an annuity problem, where you calculate the future value of a series of equal payments at regular intervals, compounded at a certain rate. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate (as a decimal), and n is the number of payments. Plugging in the values ($2000 annual payments, 11% interest rate, and 60 payments), the calculation gives a future value of approximately $9,510,132, making option A correct.

Question 20

You want to start saving for retirement. If you deposit $2,000 each year at the beginning of the next 60 years and earn 11% on the investment, how much will you have when you retire?
A) $9,510,132
B) $10,556,246
C) $792,000
D) $1,048,114

Accepted Answer

This is a problem involving the future value of a series of annuities. Since the deposits are made at the beginning of each period, we use the future value of an annuity due formula: $FV = P \times \left(\frac{(1 + r)^n - 1}{r}\right) \times (1 + r)$, where $P$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of periods. Plugging in the values: $FV = 2000 \times \left(\frac{(1 + 0.11)^{60} - 1}{0.11}\right) \times (1 + 0.11)$, we get approximately $10,556,246.

Quiz 3: Essential Concepts in Finance: Part B

Compound interest can best be described as:

To calculate the present value of an investment the following formula is used:

The future value of an investment is:

When we consider the time value of money, a dollar received in the future:

You require an 8% annual return on all investments. You have been offered an investment which will pay you $1,000 in one years time, $2,000 in two years time, and $3,000 in three years time. What is the most you would be willing to pay for this investment?

As a gift from your parents, you have just received $50,000 for your education for the next four years. You can earn an annual rate of 8% on your investments. How much can you withdraw each year (end of year) just using up the $50,000?

You borrow $95,000 for 12 years at an annual rate of 12%. What are the monthly payments required to amortize this loan?

A perpetuity can be described as:

How much would you be willing to pay for a preferred share that pays a yearly dividend of $2.80? Current yields on similar preferreds are 6%

You would like to have $500,000 put away in 20 years for your retirement. You plan to put away $14,000 each year (end of year) . What is the minimum interest rate that you would need to receive $500,000?

Calculate the present value of $100,000 received in six months. Use an annual discount rate of 10%. Do not adjust the discount rate to a semi-annual rate. Keep it annual and adjust "n" to the appropriate value.

You would like to retire with $1,000,000. You plan on a 7% annual investment rate (3.5% semi-annually) and will put away $7,500 twice a year at the end of each semi-annual period. How long before you can retire? Round to the nearest figure.

If you (1) decrease your required return and (2) decrease the number of compounding periods, what effect would this have on your present value?

What is the future value of an annuity due if your required return is 10%, and payments are $1,000 for 10 years?

To calculate the present value of an annuity due you would take the present value of an ordinary annuity answer and whereas to calculate the future value of an annuity due you would take the future value of an ordinary annuity answer and .

To settle a debt you have agreed to make payments of $200, $500, $700, $900, and $1,200 at the end of years 1- 5 respectively. The appropriate discount rate is 8%. What is the present value of your debt?

Four liters of milk cost $3.59 today. How much will it cost you to buy four liters of milk for your grandchildren in 35 years if inflation averages 5% per year?

Your parents have promised to give you $25,000 on your wedding day if you wait 10 years to get married. Your sister is getting married today. What amount should she receive in today's dollars to match your gift? The appropriate discount rate is 12%

You want to start saving for retirement. If you deposit $2000 each year at the end of the next 60 years and earn 11% on the investment, how much will you have when you retire?

You want to start saving for retirement. If you deposit $2,000 each year at the beginning of the next 60 years and earn 11% on the investment, how much will you have when you retire?