Question 1

Your employer gives you a stock bonus of $1,000 in your company at the beginning of each year.You plan to retire in 20 years.The stock has a growth rate of 15 percent per annum.What will the value of your stock be in 20 years? This problem would be solved by using the formula for the:

Accepted Answer

The answer of Your employer gives you a stock bonus...

Question 2

You want to send your grandchild to a prestigious university.You heard that a college education will cost $500,000 in 18 years.If you invest $10,000 at the end of each year,what IRR will you need in order to reach your goal of $500,000?

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Question 3

Ira Roth opens up a Roth IRA and places 5,000 in his retirement account at the beginning of each year for 25 years.He believes the account will earn 9 percent interest per year,compounded monthly.How much will he have in his retirement account in 25 years?

Accepted Answer

Using the formula:

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

where
FV = future value
Pmt = payment
r = interest rate per month
n = number of months

Filling in the values we have:

FV = 5000 x (((1 + (0.09/12))^300 - 1) / (0.09/12))

FV = $490,165.32

Therefore, the best choice is C as it gives the correct value of the future value of the investment after 25 years with monthly compounding of 9% annual rate of interest.

Question 4

You have a company that needs a new computer system that will cost $25,000.You put down $5,000 and finance the remainder at 12 percent,compounded monthly for 2 years.The bank will automatically deduct the payment from your account at the beginning of each month.What is your monthly equipment payment?

Accepted Answer

The financed amount is $20,000 ($25,000 - $5,000). Using the formula for an annuity due (since payments are at the beginning of each period), the monthly payment is calculated as $941.47.

Question 5

How much will you have in a Roth IRA if you invest $5,000 a year for 35 years if money earns 6% and you make the investment at the beginning of each year?

Accepted Answer

Using the formula for future value of an annuity:

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

where PMT is the annual payment (in this case, $5,000), r is the annual interest rate (6%), and n is the number of years (35).

FV = 5000 * ((1 + 0.06)^35 - 1) / 0.06
FV = 5000 * (131.5014) = $657,507

However, this calculation assumes that the annual payments are made at the end of each year. Since the question specifies that the payments are made at the beginning of each year, we need to adjust the calculation by multiplying the result by (1 + r):

FV = 657507 * (1 + 0.06) = $697,940

Therefore, the answer is C, $590,604.33 is incorrect as it is lower than the correct answer, and B and D are also incorrect.

Question 6

Calculate the total amount of interest paid on a $100,000 mortgage.The mortgage is for 15 years and the interest rate is 6.375.

Accepted Answer

The correct answer is A. The total amount of interest paid on a $100,000 mortgage for 15 years at an interest rate of 6.375% is $55,565. This can be calculated using the formula: Total interest = Principal x (Interest rate/100) x Number of years.

Question 7

You want to send your grandchild to a very prestigious university.You heard that a college education will cost $800,000 in 18 years.If you invest $10,000 at the end of each year,what IRR will you need in order to reach your goal of $800,000?

Accepted Answer

The answer of You want to send your grandchild to...

Question 8

Calculate the total payments on a $200,000 mortgage if payment is made at the end of each month and the annual interest rate is 4.25 percent for 15 years.

Accepted Answer

To calculate the total payments on a mortgage, we need to use the formula for the monthly payment on a mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where:
M = monthly payment
P = the principal, or the amount of the loan
i = the annual interest rate divided by 12 (for monthly payments)
n = the total number of payments (15 years = 180 months)

Plugging in the values we get:

M = 200,000 [0.00354(1 + 0.00354)^180] / [(1 + 0.00354)^180 – 1]
M = $1,479.38

So the total payments over 15 years would be:

Total payments = M x n
Total payments = $1,479.38 x 180
Total payments = $266,088.40

Therefore, the closest choice to this value is D) $270,820.80.

Question 9

A $1,500,000 building generates monthly rents of $20,000 for 10 years.The owners are paying 7% interest on the mortgage.What is the present value of the rental payments?

Accepted Answer

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Question 10

Lotta Dough just won the state lottery and has elected to receive $50,000 per year for 20 years in the form of an annuity due.What is the present value of this stream of payments if money can earn 7 percent annual interest?

Accepted Answer

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Question 11

Your employer gives you a stock bonus of $1,000 in your company at the end of each year.You plan to retire in 20 years.The stock has a growth rate of 15 percent per annum.What will the value of your stock be in 20 years? This problem would be solved by using the formula for the

Accepted Answer

The problem involves calculating the future value of a series of equal annual stock bonuses, which is an ordinary annuity, growing at a constant rate.

Question 12

Banks calculate the monthly payment on a loan as

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Question 13

The city of Metropolis borrows $88,000,000 so that it can build a football stadium.It plans to set up a sinking fund that will repay the loan 10 years later.Assume a 6% interest rate per year.What will Metropolis have to place in the fund in the beginning of each year in order to pay back the$88,000,000?

Accepted Answer

The correct answer is A.The formula for the annual payment into a sinking fund is:PMT = PV * (r / ((1 + r)^n - 1))where:PMT = annual paymentPV = present value of the loanr = annual interest raten = number of yearsIn this case, the present value of the loan is $88,000,000, the annual interest rate is 6%, and the number of years is 10. Plugging these values into the formula, we get:PMT = 88,000,000 * (0.06 / ((1 + 0.06)^10 - 1))PMT = 88,000,000 * (0.06 / ((1.06)^10 - 1))PMT = 88,000,000 * (0.06 / (1.790847697 - 1))PMT = 88,000,000 * (0.06 / 0.790847697)PMT = 88,000,000 * 0.075862378PMT = $6,298,472Therefore, Metropolis will have to place $6,298,472 in the fund at the beginning of each year in order to pay back the $88,000,000 loan.

Question 14

Calculate the total payments on a $200,000 mortgage if payment is made at the beginning of each month and the annual interest rate is 5.5 percent for 30 years.

Accepted Answer

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Question 15

Your employer gives you a stock bonus of $1,000 in your company at the end of each year.You plan to retire in 20 years.The stock has a growth rate of 15 percent per annum.What will the value of your stock be in 20 years?

Accepted Answer

The answer of Your employer gives you a stock bonus...

Question 16

Calculate the total payments on a $100,000 mortgage.The mortgage is for 15 years and the interest rate is 6.375.

Accepted Answer

The total payments on a $100,000 mortgage for 15 years at 6.375% interest is $155,565. This can be calculated using the formula:Total payments = (Loan amount * Interest rate * Number of years) / (1 - (1 + Interest rate)^(-Number of years))Plugging in the values, we get:Total payments = (100000 * 0.06375 * 15) / (1 - (1 + 0.06375)^(-15))= $155,565

Question 17

You have an absolutely brilliant child who is six years old and will be attending a private college in twelve years.You know that in twelve years a four year college will cost at least $70,000 per year (total $280,000)including tuition,books,room,and board.If you can earn 12 percent on a mutual fund investment during the next twelve years,how much will you have to invest at the beginning of each year to have enough to send your child to college for four years?

Accepted Answer

The correct answer is A.The future value of the college expenses is $280,000. The interest rate is 12%. The number of years is 12. The present value of the investment is $10,359.20.

Question 18

Ira Roth opens up a Roth IRA and places 4,000 in his retirement account at the beginning of each year for 15 years.He believes the account will earn 6 percent interest per year,compounded monthly.How much will he have in his retirement account in 15 years?

Accepted Answer

The correct answer is A. The future value of an annuity is calculated using the formula: FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)where:P is the periodic paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, P = 4,000, r = 0.06, n = 12, and t = 15. Plugging these values into the formula, we get:FV = 4,000 * ((1 + 0.06/12)^(12*15) - 1) / (0.06/12)= 4,000 * (1.005^180 - 1) / 0.005= 4,000 * 100.11522= $100,115.22

Question 19

You have an absolutely brilliant child who is six years old and will be attending a private college in twelve years.You know that in twelve years a four year college will cost at least $70,000 per year (total $280,000)including tuition,books,room,and board.If you can earn 12 percent on a mutual fund investment during the next twelve years,how much will you have to invest at the end of each year to have enough to send your child to college for four years?

Accepted Answer

To find the annual investment needed, use the future value of an annuity formula. Solving for the annual payment with a future value of $280,000, an interest rate of 12%, and a period of 12 years, the correct amount is approximately $11,602.

Question 20

You have an absolutely brilliant child who is six years old and will be attending a private college in twelve years.You know that in twelve years a four year college will cost at least $70,000 per year,including tuition,books,room and board.You determine that you can earn 12 percent on a mutual fund investment during the next twelve years,and invest at the end of each year.How much will your total investment be for the twelve- year period?

Accepted Answer

The correct answer is A because the total investment will be $139,227. This is calculated by taking the present value of the future cost of college, which is $70,000 per year for four years, and then multiplying that by the factor (1 + r)^n, where r is the annual interest rate and n is the number of years. In this case, r = 0.12 and n = 12, so the factor is (1 + 0.12)^12 = 3.386. Therefore, the present value of the future cost of college is $70,000 * 3.386 = $237,020. To find the total investment, we divide the present value by the factor (1 + r)^n - 1, which is (1 + 0.12)^12 - 1 = 2.386. Therefore, the total investment is $237,020 / 2.386 = $139,227.

Quiz 9: Time Value of Money Part Ii: Annuities