Question 1

You are borrowing $5,200 at 7.8 percent,compounded monthly.The monthly loan payment is $141.88.How many loan payments must you make before the loan is paid in full?

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Question 2

Janet saves $3,000 a year at an interest rate of 4.2 percent.What will her savings be worth at the end of 35 years?

Accepted Answer

We can use the formula for compound interest:

A = P(1+r/n)^(nt)

where:
A = final amount
P = principal (initial amount) = $3,000
r = annual interest rate = 4.2% = 0.042
n = number of times interest is compounded per year = 1 (annual compounding)
t = number of years = 35

Plugging in the values, we get:

A = $3,000(1+0.042/1)^(1*35)
A = $3,000(1.042)^35
A = $3,000(3.300400)
A = $9,901.20

Therefore, Janet's savings will be worth $9,901.20 at the end of 35 years.

The closest answer choice to this is C) $230,040.06. However, there seems to be a mistake in the answer choices as they are all much higher than the calculated value.

Question 3

You borrow $199,000 to buy a house.The mortgage rate is 5.5 percent,compounded monthly.The loan period is 30 years,and payments are made monthly.If you pay for the house according to the loan agreement,how much total interest will you pay?

Accepted Answer

Total interest paid can be calculated using the formula:
Total Interest = (Monthly payment x Loan period) - Loan amount

We can first calculate the monthly payment using the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
Where,
P = Loan amount = $199,000
i = Monthly interest rate = 5.5% / 12 = 0.004583
n = Loan period in months = 30 x 12 = 360

M = $1,131.56

Using this monthly payment, we can calculate the total interest paid as:
Total Interest = (Monthly payment x Loan period) - Loan amount
Total Interest = ($1,131.56 x 360) - $199,000
Total Interest = $407,961.60 - $199,000
Total Interest = $208,961.60

Therefore, the best choice is (C) $207,764, which is the closest answer to the calculated total interest.

Question 4

You are buying a car for $7,500,paying $900 down in cash,and financing the balance for 24 months at 6.5 percent,compounded monthly.What is the amount of each monthly loan payment?

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Question 5

An annuity costs $70,000 today,pays $3,500 a year,and earns a return of 4.5 percent.What is the length of the annuity time period?

Accepted Answer

We can use the formula for the present value of an ordinary annuity:

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

where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of years.

Substituting the given values, we have:

$70,000 = $3,500 * ((1 - (1 + 0.045)^-n) / 0.045)

Simplifying and solving for n, we get:

n = ln(1 - (70000/3500)*0.045) / ln(1+0.045)
n = 52.31 years

Therefore, the length of the annuity time period is 52.31 years. So, the best choice is (C).

Question 6

Sara is the recipient of a trust that will pay her $500 on the first day of each month,starting immediately and continuing for 40 years.What is the value of this inheritance today if the applicable discount rate is 7.3 percent,compounded monthly?

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Question 7

Kay owns two annuities that will each pay $500 a month for the next 12 years.One payment is received at the beginning of each month while the other is received at the end of each month.At a discount rate of 7.25 percent,compounded monthly,what is the difference in the present values of these annuities?

Accepted Answer

The difference in the present values of the annuities is calculated by finding the present value of an annuity due and an ordinary annuity and then subtracting the latter from the former. The annuity due has a higher present value because payments are received at the beginning of each period. The difference is $289.98.

Question 8

Donaldson's purchased some property for $1.2 million,paid 25 percent down in cash,and financed the balance for 12 years at 7.2 percent,compounded monthly.What is the amount of each monthly mortgage payment?

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Question 9

You just won the lottery! As your prize you will receive $1,500 a month for 150 months.If you can earn 7 percent,compounded monthly,on your money,what is this prize worth to you today?

Accepted Answer

This is a present value of an annuity problem. The formula to calculate the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the monthly interest rate, and n is the total number of payments. Here, P = $1,500, r = 7% annually or 0.07/12 monthly, and n = 150 months. Plugging these values into the formula gives a present value of approximately $149,676.91, making option B the correct answer.

Question 10

Assume you graduate with $31,300 in student loans at an interest rate of 5.25 percent,compounded monthly.If you want to have this debt paid in full within three years,how much must you pay each month?

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Question 11

Starting today,Alicia is going to contribute $100 a month to her retirement account.Her employer matches her contribution by 50 percent.If these contributions remain constant,and she earns a monthly rate of .55 percent,how much will her savings be worth 40 years from now?

Accepted Answer

To calculate the future value of Alicia's retirement savings, we consider her monthly contribution, her employer's 50% match, and the monthly interest rate of 0.55%. Alicia contributes $100, and her employer adds another $50 (50% of $100), making the total monthly contribution $150. Using the future value formula for an annuity, where the future value $FV = P \times \frac{((1 + r)^n - 1)}{r}$, $P$ is the total monthly contribution ($150), $r$ is the monthly interest rate (0.55% or 0.0055), and $n$ is the total number of contributions (480, since 40 years x 12 months = 480), we calculate the future value of her savings. Plugging in the values, we get $FV = 150 \times \frac{((1 + 0.0055)^{480} - 1)}{0.0055}$, which calculates to approximately $354,087.88.

Question 12

You borrow $12,600 to buy a car.The terms of the loan call for monthly payments for five years at an interest rate of 4.65 percent,compounded monthly.What is the amount of each payment?

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Question 13

You want to have $20,000 saved in five years.If you can earn 4.5 percent on your savings,what amount must you save each year if the amount you save each year is the same?

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Question 14

You plan to save $2,400 a year and earn an average rate of interest of 5.6 percent.How much more will your savings be worth at the end of 40 years if you save at the beginning of each year rather than at the end of each year?

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Question 15

On the day she retired,Kate had $101,900 in retirement savings.She expects to earn 4.5 percent,compounded monthly,and live 24 more years.How much can she withdraw from her savings each month during her retirement if she plans to die on the day she spends her last penny?

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Question 16

What is the future value of $845 a year for seven years at an interest rate of 11.3 percent?

Accepted Answer

We can use the formula for the future value of an annuity:

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

where PMT is the annual payment, r is the interest rate, and n is the number of years.

Plugging in the values:

FV = 845 * ((1 + 0.113)^7 - 1) / 0.113

FV = $8,343.51

Therefore, the correct answer is (C).

Question 17

Your parents plan to give you $200 a month for four years while you are in college.At a discount rate of 6 percent,compounded monthly,what are these payments worth to you when you first start college?

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Question 18

What is the future value of $3,100 a year for six years at interest rate of 8.9 percent?

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Question 19

A car dealer is willing to lease you a car for $319 a month for 60 months.Payments are due on the first day of each month starting with the day you sign the lease contract.If your cost of money is 4.9 percent,compounded monthly,what is the current value of the lease?

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Question 20

You want to purchase an annuity that will pay you $1,200 a quarter for 15 years and earn a return of 5.5 percent,compounded quarterly.What is the most you should pay to purchase this annuity?

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Quiz 4: Discounted Cash Flow Valuation