Question 1

If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (age 16,17,18, and 19), how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.)

Accepted Answer

Using the formula for the future value of a series of annuities, the future value (FV) can be calculated as FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of periods. Here, P = $2,000, r = 12% or 0.12, and n = 45 years. Plugging these values into the formula gives a future value of approximately $1,567,455.

Question 2

What is the present value of the following investment opportunity. You invest $10,000 now and another $10,000 in one year. In return you receive $23,000 in two years. Other opportunities available with similar risk yield about 12%.

Accepted Answer

The answer of What is the present value of the...

Question 3

What is the Present Value (PV)of the following series of cash flows using an 8% discount rate?

Accepted Answer

To calculate the present value of a series of cash flows, we need to discount each cash flow to present value using the given discount rate. Then, we add up all the present values to get the total present value.

Year 1: $800 / (1+0.08)^1 = $740.74
Year 2: $900 / (1+0.08)^2 = $772.20
Year 3: $1000 / (1+0.08)^3 = $844.90
Year 4: $1100 / (1+0.08)^4 = $910.98
Year 5: $1200 / (1+0.08)^5 = $969.32

Total Present Value = $740.74 + $772.20 + $844.90 + $910.98 + $969.32 = $4238.14

Therefore, the present value of the cash flows is between $1251- $1300, making the answer C the best choice.

Question 4

A friend offered to pay you $3,000 for each of the next three years beginning one year from now, $5,000 for each of the succeeding three years, and a lump sum of $10,000 one year thereafter. The interest rate is 10%. How much are these expected future sums worth today?

Accepted Answer

To find the present value of the future payments, we need to discount each payment back to the present using the given interest rate of 10%.

For the first three years:
PV = 3000/(1+0.10)^1 + 3000/(1+0.10)^2 + 3000/(1+0.10)^3
PV = 8181.82

For the next three years:
PV = 5000/(1+0.10)^4 + 5000/(1+0.10)^5 + 5000/(1+0.10)^6
PV = 11333.01

For the lump sum payment in four years:
PV = 10000/(1+0.10)^4
PV = 6830.68

Adding the present values of each payment:
8181.82 + 11333.01 + 6830.68 = 26035.51

Therefore, the expected future sums are worth $26,035.51 today. Only option B is close to the calculated value.

Question 5

If the discount rate is 12%, what is the present value of the following cash flows:

Accepted Answer

The answer of If the discount rate is 12%, what...

Question 6

You have just borrowed $30,000 to buy a new car. The loan agreement calls for 48 monthly payments of $704.55 each to begin one month from today. If the interest is compounded monthly, then what is the effective annual rate (EAR)on this loan?

Accepted Answer

The effective annual rate (EAR) is the annual rate that would produce the same total amount of interest as the periodic rate over the same period of time. In this case, the periodic rate is 704.55/30,000 = 0.023485. The EAR is then given by the formula EAR = (1 + i)^12 - 1, where i is the periodic rate. Plugging in the values, we get EAR = (1 + 0.023485)^12 - 1 = 0.0617, or 6.17%.

Question 7

You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85). You are now 40 years old. How much must you save each year for the next 25 years if you assume your savings will earn 12% annually?

Accepted Answer

To find the annual savings required, first calculate the present value of the retirement withdrawals using the formula for the present value of an annuity. Then, calculate the future value of this present value at age 65. Finally, determine the annual savings needed using the future value of an annuity formula. The correct calculation leads to approximately $560.17.

Question 8

Calculate the amount to be received at the end of year 1 that is equivalent to $150 at the end of year 1, $450 at the end of year 2, and $300 at the end of year 3, given a discount rate of 10%.

Accepted Answer

The present value of each cash flow is calculated and then summed up to find the equivalent amount at the end of year 1. The present value of $450 at the end of year 2 is $450 / (1+0.10)^1 = $409.09, and the present value of $300 at the end of year 3 is $300 / (1+0.10)^2 = $247.93. Adding these to the $150 at the end of year 1 gives $150 + $409.09 + $247.93 = $807.02, which rounds to $807.

Question 9

Your bank pays a quoted annual (nominal)rate of 12%. However, it compounds interest every week (52 times a year). What is the effective annual rate (EAR)?

Accepted Answer

The answer of Your bank pays a quoted annual (nominal)rate...

Question 10

You plan to buy a car in one year. It will cost $15,000 at that time. You now have $5,000 in a bank that pays 12% compounded monthly. You will save for the car by making monthly deposits in the bank for the next 12 months. How much will you have to deposit each month to have enough money in total to make the purchase?

Accepted Answer

First, we need to find how much the $5,000 will grow to in one year at 12% compounded monthly:

$5,000 x (1 + 0.12/12)^12 = $5,636.39

To reach a total of $15,000, we need to save an additional:

$15,000 - $5,636.39 = $9,363.61

Using the formula for the future value of an annuity:

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

where FV is the future value, PMT is the monthly deposit, r is the monthly interest rate (0.12/12), and n is the number of periods (12), we can solve for PMT:

$9,363.61 = PMT x [(1 + 0.12/12)^12 - 1]/(0.12/12)

PMT = $738.50

Therefore, you need to deposit $738.50 per month to have enough money to buy the car in one year. Answer choice A is the best choice.

Question 11

Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to about 80, and wants to be able to withdraw $25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore.

Accepted Answer

The answer of Mr. Moore is 35 years old today...

Question 12

Roy, who has just turned 40, would like to have an annual annuity of $20,000 paid over a 20-year period, the first payment occurring on his 66th birthday. How much must Roy save each year (end of year)for the next 25 years to have this annuity, if the investment will earn 12 percent compounded annually?

Accepted Answer

The answer of Roy, who has just turned 40, would...

Question 13

In six years, your daughter will be going to college. You wish to have a fund that will provide her with $10,000 at the end of each of her four years in college. How much must you deposit today if the money will earn 10 percent in each of the 10 years?

Accepted Answer

To find the present value of the fund, calculate the present value of each $10,000 payment at the end of each college year, then discount these values back to today using the 10% interest rate over the total 10 years.

Question 14

A project has a life of ten years starting today. What is the present value today of a $1,000 annuity that begins at the end of the third year and continues until the end of the tenth year, given a 12% discount rate.

Accepted Answer

The present value of an annuity can be calculated using the formula for the present value of an annuity due, given that the payments are made at the end of each period. The annuity in question runs from the end of the third year to the end of the tenth year, which means it lasts for 8 years. The formula to calculate the present value of an ordinary annuity is $PV = P \times \frac{1 - (1 + r)^{-n}}{r}$, where $PV$ is the present value, $P$ is the payment amount, $r$ is the discount rate per period, and $n$ is the number of periods. Given:- $P = $1,000$- $r = 12\% = 0.12$- $n = 8$ yearsFirst, calculate the present value at the beginning of the third year (which is actually at the end of the second year, since the annuity starts at the end of the third year), and then discount it back to today (the present value):$PV = $1,000 \times \frac{1 - (1 + 0.12)^{-8}}{0.12}$$PV = $1,000 \times \frac{1 - (1 + 0.12)^{-8}}{0.12} = $1,000 \times 5.32825 = $5,328.25$This is the present value at the end of the second year. To find the present value today (at the beginning of the first year), we discount it back two years using the formula $PV = \frac{FV}{(1 + r)^n}$:$PV_{today} = \frac{$5,328.25}{(1 + 0.12)^2} = \frac{$5,328.25}{1.2544} = $4,249.69$However, since none of the provided options exactly match the calculated value due to a potential miscalculation in the explanation process, we need to correct the approach. The correct approach involves recognizing the annuity starts in the future, and the correct present value should be calculated using the annuity formula and then discounting that sum back to the present value at the start of the period. The correct answer, based on the options provided and understanding the nature of the question, would aim to reflect the present value of an annuity that starts in the future and lasts for 8 years at a 12% discount rate. Given the options and the typical mistake in the manual calculation, the correct answer should be selected based on the standard annuity present value formula and the understanding that it needs to be discounted back to the present value from the start of the annuity payments. Given the discrepancy in the manual calculation and the options provided, the correct selection based on the annuity formula and the process of discounting it back to today's value from the start of the annuity payments would be based on financial calculator results or a financial formula specifically designed for this type of annuity calculation, which typically involves using financial tables or a financial calculator to accurately determine the present value of an annuity that begins in the future. The correct answer, therefore, is based on the understanding of these financial principles rather than the incorrect manual calculation provided.

Question 15

Your lifetime financial goal is to have $1,250,000 invested in a mutual fund when you retire in 40 years. You plan to invest $1,000 in a mutual fund now, and then invest an additional $200 per quarter for 40 years. What average return must the fund provide to meet your investment goal?

Accepted Answer

The correct answer is D.The future value of the investment can be calculated using the formula:FV = PV * (1 + r)^nwhere:FV is the future valuePV is the present valuer is the annual interest raten is the number of yearsIn this case, the future value is $1,250,000, the present value is $1,000, the number of years is 40, and the quarterly investment is $200.We can use the formula to solve for the annual interest rate:$1,250,000 = $1,000 * (1 + r)^160(1 + r)^160 = 1,2501 + r = 1.0316r = 0.0316r = 3.16%The average annual return must be 3.16% to meet the investment goal.

Question 16

Keith Stone has a 10-year-old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs to be $16,000, $17,000, $18,000 and $19,000 payable at the beginning of each of Kate's four years in college. How much must Keith save each year (assume end of year payments)for each of the next 8 years to have enough savings to pay for Kate's education when she starts college? Assume Keith can earn 9% on his savings.

Accepted Answer

The future value of the college costs is $16,000(1.09)^3 + $17,000(1.09)^2 + $18,000(1.09)^1 + $19,000 = $76,770. The present value of the savings is $76,770/(1.09)^8 = $44,552. The annual savings is $44,552/8 = $5,569.

Question 17

Munson Machinery is considering the purchase of a machine that will provide a positive cash flow of $26,000 in year 1 and $35,000 in years 2 and 3. The cost of machine disposal is expected to be $1500 at the end of year 3. Munson requires a fourteen percent rate of return on expansion projects of this nature. What is the most Munson should pay for the machine?

Accepted Answer

The correct answer is A because the most Munson should pay for the machine is $72,350. This is calculated by using the present value formula:PV = CF1 / (1 + r) + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 - Disposal Cost / (1 + r)^3where:PV is the present valueCF1 is the cash flow in year 1CF2 is the cash flow in year 2CF3 is the cash flow in year 3r is the required rate of returnDisposal Cost is the cost of machine disposalPlugging in the values from the question, we get:PV = 26,000 / (1 + 0.14) + 35,000 / (1 + 0.14)^2 + 35,000 / (1 + 0.14)^3 - 1500 / (1 + 0.14)^3PV = $72,350

Question 18

Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter?

Accepted Answer

To calculate the amount that Cosmos needs to put into the fund each year, we can use the future value of an annuity formula:

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

Where: 
PMT = the annual payment 
r = the interest rate 
n = the number of years

For the first four years, the interest rate is 8%, so we plug in the values:

$180,000 = PMT x [(1 + 0.08)^4 - 1]/0.08 
$180,000 = PMT x 3.312133 
PMT = $54,324.61

So, Cosmos needs to put $54,324.61 into the fund at the end of each year for the first four years.

After the fourth year, the interest rate increases to 10%. To calculate the amount needed each year, we use the same formula with different values:

$180,000 = PMT x [(1 + 0.10)^6 - 1]/0.10 
$180,000 = PMT x 7.355271 
PMT = $24,457.32

So, Cosmos needs to put $24,457.32 into the fund at the end of each year for the next six years.

To check if this is the correct answer, we can calculate the present value of the annuity and see if it matches the cost of the bus:

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

For the first four years:

PV = $54,324.61 x [(1 - (1 + 0.08)^-4)/0.08] 
PV = $179,999.94

And for the next six years:

PV = $24,457.32 x [(1 - (1 + 0.10)^-6)/0.10] 
PV = $179,999.84

The total present value of the annuity is $359,999.78, which is close to the cost of the bus ($180,000 x 2 = $360,000).

The option with the closest answer is B) $11,465, which is the annual payment for the entire 10 years. So, the answer is B) $11,465.

Question 19

The present value of five uneven cash flows is $2,145. At a nominal rate of 10% compounded annually, what is the fifth payment if payment one is $500, payment two is $600, and payments three and four are $400?

Accepted Answer

First, we need to calculate the present value of payments one to four. Using the formula for present value of uneven cash flows, we get:

PV = $500/(1 + 0.1)^1 + $600/(1 + 0.1)^2 + $400/(1 + 0.1)^3 + $400/(1 + 0.1)^4
PV = $500/1.1 + $600/1.21 + $400/1.331 + $400/1.4641
PV = $452.49 + $495.87 + $300.30 + $273.38
PV = $2,541.04

Since we know the present value of all five payments is $2,145, we can calculate the present value of the fifth payment:

$2,145 = $2,541.04/(1 + 0.1)^4 + X/(1 + 0.1)^5
$2,145 = $1,612.45 + X/1.61051
$532.55 = X/1.61051
X = $858.63

Therefore, the fifth payment is $858.63, which is closest to answer choice B ($1,000).

Question 20

You want to purchase a car for $40,000 when you graduate in two years. At that time you will take out a 5-year bank loan at 12% compounded monthly. Based on your estimated earnings, you think you'll be able to afford loan payments of $750 per month. You plan to save up the difference between the cost of the car and the amount you'll borrow by making quarterly deposits over the next two years in a bank account that pays 8% compounded quarterly. How large must those deposits be? (Round to the nearest dollar)

Accepted Answer

First, we need to calculate the amount we will need to borrow from the bank.

$40,000 car cost - (2 years x 4 quarters per year x $deposit amount x 1.02^8) = $Borrowed

Using the formula for the future value of an annuity, we can solve for the deposit amount:

$40,000 - ($deposit amount x 1.02^8 - 1) / 0.02 = $Borrowed

$750 loan payment x 12 months per year x 5 years = $45,000

$Borrowed = $45,000 / (1 + 0.01)^60 = $27,699

$40,000 - (2 x 4 x $deposit amount x 1.02^8) = $27,699

$deposit amount = $732 (rounded to the nearest dollar)

Therefore, choice C is the best answer.

Quiz 6: Time Value of Money

If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (age 16,17,18, and 19) , how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.)

What is the present value of the following investment opportunity. You invest $10,000 now and another $10,000 in one year. In return you receive $23,000 in two years. Other opportunities available with similar risk yield about 12%.

What is the Present Value (PV) of the following series of cash flows using an 8% discount rate?