Question 1

An annuity will pay you $5,000 per year for 25 years.What is the FV of this annuity at the end of 25 years,if your interest rate is 8%?

Accepted Answer

To find the future value (FV) of the annuity, we can use the formula: FV = PMT x (((1+i)^n-1)/i), where PMT is the annual payment, i is the interest rate per period, and n is the number of periods. In this case, PMT = $5,000, i = 8%, and n = 25. Plugging in these values, we get:
FV = $5,000 x (((1+0.08)^25-1)/0.08) = $365,530
Therefore, the FV of the annuity is $365,530 at the end of 25 years, and the best choice is B.

Question 2

Since your first birthday,your grandparents have been depositing $1000 into a savings account on every one of your birthdays.The account pays 4% interest annually.Immediately after your grandparents make the deposit on your 18th birthday,the amount of money in your savings account will be closest to:

Accepted Answer

The correct answer is A because the amount of money in the savings account after 18 years is $25,645. This is calculated by taking the initial deposit of $1000 and multiplying it by the number of years (18), which gives us $18,000. Then, we add the interest earned over 18 years, which is $7,645. This gives us a total of $25,645.

Question 3

An annuity will pay you $1,000 per year for 30 years.What is the FV of this annuity at the end of 30 years,if your cost of capital is 3%?

Accepted Answer

FV of annuity = PMT * [(1 + r)^n - 1] / r= 1000 * [(1 + 0.03)^30 - 1] / 0.03= 1000 * [2.42725 - 1] / 0.03= 1000 * 1.42725 / 0.03= 47,575

Question 4

An annuity will pay you $12,000 per year for 20 years.What is the PV of this annuity if your cost of capital is 7%?

Accepted Answer

To find the present value of an annuity, we can use the formula:

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

Where: 
C = annual cash flow 
r = discount rate 
n = number of years

In this case, C = $12,000, r = 7%, and n = 20. Plugging these values into the formula, we get:

PV = $12,000 x [(1 - (1 / (1 + 0.07)^20)) / 0.07]
PV = $127,128

Therefore, the correct answer is (C).

Question 5

James is a law student who wishes to understand how a perpetuity works.His grandfather invested in a perpetual bond 25 years ago,which pays $15,000 annually at a 12% interest rate.What was the present value of the cash flows of this perpetuity when it was purchased?

Accepted Answer

The answer of James is a law student who wishes...

Question 6

If the current rate of interest is 8%,then the future value (FV)of an investment that pays $1000 per year and lasts 20 years is closest to:

Accepted Answer

We can use the formula for annuity (regular payments) to calculate the future value:
FV = PMT * ((1+r)^n - 1)/r
where PMT is the regular payment, r is the annual interest rate, and n is the number of periods (years in this case).

Substituting the values, we get:
FV = 1000 * ((1+0.08)^20 - 1)/0.08
FV = 45,762

Therefore, the closest answer is B, $45,762.

Question 7

Since your first birthday,your grandparents have been depositing $100 into a savings account every month.The account pays 4% interest annually.Immediately after your grandparents make the deposit on your 18th birthday,the amount of money in your savings account will be closest to:

Accepted Answer

The future value of a series of monthly deposits can be calculated using the future value of an annuity formula. With monthly deposits of $100, an annual interest rate of 4% (or 0.3333% monthly), and 216 deposits (18 years), the future value is closest to $31,559.

Question 8

Jackie and her husband started a savings account for their twin daughters when they were 2 years old.They have been saving $100,000 a year at an interest rate of 10%,and intend on keeping up with their annual contribution to the fund until the girls are 21.What is the future value of their investment?

Accepted Answer

We can use the formula for future value of ordinary annuity to solve this problem:

FV = PMT x (((1 + r)^n - 1) / r)

Where:
PMT = $100,000 (annual contribution)
r = 10% (interest rate)
n = 20 (number of years until the girls turn 21)

FV = $100,000 x (((1 + 0.10)^20 - 1) / 0.10) = $5,115,909.05

Therefore, the future value of their investment is $5,115,909.05, which is option C.

Question 9

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the future value (FV)of this perpetuity,given that the interest rate is 4%?

Accepted Answer

A perpetuity by definition pays an infinite series of payments. Therefore, it does not have a future value in the traditional sense, as it does not "end" to calculate a future value at a specific point in time.

Question 10

If the current rate of interest is 8%,then the present value (PV)of an investment that pays $1000 per year and lasts 20 years is closest to:

Accepted Answer

The answer of If the current rate of interest is...

Question 11

Which of the following is TRUE about perpetuities?

Accepted Answer

If two perpetuities have the same present value and the same interest rate, they must have the same cash flows, as the present value of a perpetuity is determined by dividing the cash flow by the interest rate.

Question 12

Anya finally decides that she will give her cousin,Zen,the loan he requested.He is expected to pay Anya $12,500 each year for the next 5 years,starting at the end of this year.The loan interest rate at the bank is 5% but because he is family,she will only charge him half of this interest rate.What is the current value of this loan,today?
  B)$500,000 C)$62,500 D)$54,118.46 E)$55,240.89

Accepted Answer

The answer of Anya finally decides that she will give...

Question 13

Jason buys a consol (perpetual bond)that pays out a fixed cash flow of $750,000 every year,forever,starting at the end of this year.If the current market rate is 12.5%,what is the present value of the cash flows?

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = C / r, where C is the annual cash flow and r is the discount rate. Here, C = $750,000 and r = 12.5% or 0.125. Thus, PV = $750,000 / 0.125 = $6,000,000.

Question 14

Matthew wants to take out a loan to buy a car.He calculates that he can make repayments of $4000 per year.If he can get a five-year loan with an interest rate of 7.5%,what is the maximum price he can pay for the car?

Accepted Answer

The maximum price Matthew can pay for the car is $16,184. This is calculated using the formula:Loan amount = (Repayment amount * (1 - (1 + interest rate)^-number of years)) / interest rateIn this case, the repayment amount is $4000, the interest rate is 7.5%, and the number of years is 5. Plugging these values into the formula, we get:Loan amount = (4000 * (1 - (1 + 0.075)^-5)) / 0.075= (4000 * (1 - 0.6830)) / 0.075= (4000 * 0.3170) / 0.075= 16,184

Question 15

JJ & Co has decided to donate money to a cancer research fund every year for the next 25 years.They will make annual payments of $3.5 million.What is the present value of their donation if the current market rate is 7.5%?

Accepted Answer

The answer of JJ & Co has decided to donate...

Question 16

You are saving money for the down payment on a house.If you can save $7,500 per year for the next five years at an interest rate of 8%,how much will you have saved at the end of five years?

Accepted Answer

This is a compound interest problem where you save $7,500 annually at an 8% interest rate for 5 years. Using the future value of a series formula: FV = P * [(1 + r)^n - 1] / r, where P = annual payment, r = annual interest rate, n = number of years, we calculate the future value of these annual savings. Plugging in the values: FV = 7500 * [(1 + 0.08)^5 - 1] / 0.08, we get approximately $44,000.

Question 17

An annuity will pay you $1,000 per year for 75 years.What is the PV of this annuity if your cost of capital is 4%?

Accepted Answer

The answer of An annuity will pay you $1,000 per...

Question 18

Which of the following is TRUE about perpetuities?

Accepted Answer

A perpetuity generates cash flows every period infinitely, and each cash flow is equal to the amount of the payment. Therefore, the total cash flow generated equals the present value of the perpetuity multiplied by the interest rate.

Question 19

You are borrowing money to buy a car.If you can make payments of $300 per month starting one month from now at an interest rate of 4%,how much will you be able to borrow for the car today if you finance the amount over four years?

Accepted Answer

The answer of You are borrowing money to buy a...

Question 20

You are saving money to buy a car.If you save $300 per month starting one month from now at an interest rate of 4%,how much will you be able to spend on the car after saving for 4 years?

Accepted Answer

Using the formula for future value of an annuity,

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

where PMT is the monthly savings amount, r is the monthly interest rate (4% / 12 = 0.00333), and n is the number of months (4 years x 12 months = 48).

FV = (300 x [(1 + 0.00333)^48 - 1]) / 0.00333 = $15,587.88

Therefore, you will be able to spend $15,587.88 on the car after saving for 4 years.

Quiz 4: The Time Value of Money

An annuity will pay you $5,000 per year for 25 years.What is the FV of this annuity at the end of 25 years,if your interest rate is 8%?

An annuity will pay you $1,000 per year for 30 years.What is the FV of this annuity at the end of 30 years,if your cost of capital is 3%?

An annuity will pay you $12,000 per year for 20 years.What is the PV of this annuity if your cost of capital is 7%?

James is a law student who wishes to understand how a perpetuity works.His grandfather invested in a perpetual bond 25 years ago,which pays $15,000 annually at a 12% interest rate.What was the present value of the cash flows of this perpetuity when it was purchased?

If the current rate of interest is 8%,then the future value (FV) of an investment that pays $1000 per year and lasts 20 years is closest to:

Since your first birthday,your grandparents have been depositing $100 into a savings account every month.The account pays 4% interest annually.Immediately after your grandparents make the deposit on your 18th birthday,the amount of money in your savings account will be closest to:

A perpetuity will pay $1000 per year,starting five years after the perpetuity is purchased.What is the future value (FV) of this perpetuity,given that the interest rate is 4%?

If the current rate of interest is 8%,then the present value (PV) of an investment that pays $1000 per year and lasts 20 years is closest to:

Which of the following is TRUE about perpetuities?

Jason buys a consol (perpetual bond) that pays out a fixed cash flow of $750,000 every year,forever,starting at the end of this year.If the current market rate is 12.5%,what is the present value of the cash flows?

Matthew wants to take out a loan to buy a car.He calculates that he can make repayments of $4000 per year.If he can get a five-year loan with an interest rate of 7.5%,what is the maximum price he can pay for the car?

JJ & Co has decided to donate money to a cancer research fund every year for the next 25 years.They will make annual payments of $3.5 million.What is the present value of their donation if the current market rate is 7.5%?

You are saving money for the down payment on a house.If you can save $7,500 per year for the next five years at an interest rate of 8%,how much will you have saved at the end of five years?

An annuity will pay you $1,000 per year for 75 years.What is the PV of this annuity if your cost of capital is 4%?

Which of the following is TRUE about perpetuities?

You are borrowing money to buy a car.If you can make payments of $300 per month starting one month from now at an interest rate of 4%,how much will you be able to borrow for the car today if you finance the amount over four years?

You are saving money to buy a car.If you save $300 per month starting one month from now at an interest rate of 4%,how much will you be able to spend on the car after saving for 4 years?