Question 1

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year.How much would be in the account after 8 months,assuming each month has 30 days?
A) $5,178.09
B) $5,436.99
C) $5,708.84
D) $5,994.28
E) $6,294.00

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In this case, P = $5,000, r = 5.25% or 0.0525, n = 360 (daily compounding), and t = 8/12 years (since 8 months is 8/12 of a year). Plugging these values into the formula gives A = 5000(1 + 0.0525/360)^(360*(8/12)), which calculates to approximately $5,178.09.

Question 2

Billy Thornton borrowed $20,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Billy have to pay in a 30-day month?
A) $120.83
B) $126.88
C) $133.22
D) $139.88
E) $146.87

Accepted Answer

The answer of Billy Thornton borrowed $20,000 at a rate...

Question 3

You plan to borrow $35,000 at a 7.5% annual interest rate.The terms require you to amortize the loan with 7 equal end-of-year payments.How much interest would you be paying in Year 2?
A) $1,994.49
B) $2,099.46
C) $2,209.96
D) $2,326.27
E) $2,442.59

Accepted Answer

To solve this problem, we need to use the amortization formula:

Payment = (P x r) / (1 - (1 + r)^-n)

where:
P = the principal (amount borrowed) = $35,000
r = the interest rate per period = 7.5% / 1 = 0.075
n = the total number of periods = 7

Using this formula, we can calculate the payment amount:

Payment = (35,000 x 0.075) / (1 - (1 + 0.075)^-7) 
Payment = $6,275.07

This means you'll pay $6,275.07 at the end of each year for 7 years.

To calculate the interest paid in Year 2, we need to first calculate the remaining balance at the end of Year 1. We can use the following formula to calculate the remaining balance:

Remaining balance = P x (1 + r)^n - Payment x ((1 + r)^n - 1) / r

where:
n = the number of payments made = 1
Payment = $6,275.07
r = 0.075
P = $35,000

Remaining balance = 35,000 x (1 + 0.075)^1 - 6,275.07 x ((1 + 0.075)^1 - 1) / 0.075
Remaining balance = $29,003.75

So, in Year 2, you'll pay interest on a balance of $29,003.75. To calculate the interest, we can use the following formula:

Interest = Balance x r

where:
Balance = $29,003.75
r = 0.075

Interest = $29,003.75 x 0.075 
Interest = $2,175.28

Therefore, the correct answer is D) $2,326.27.

Question 4

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years.How large would your payments be?
A) $3,704.02
B) $3,889.23
C) $4,083.69
D) $4,287.87
E) $4,502.26

Accepted Answer

This is a problem of calculating the payment for an installment loan, which can be solved using the formula for the annuity payment or an amortization calculator. Given a principal of $12,000, an annual interest rate of 9.0%, and a term of 4 years, the correct payment amount is $3,704.02. This calculation takes into account the interest on the declining balance over the period, ensuring that both the principal and the interest are fully paid off over the 4 years.

Question 5

Your cousin will sell you his coffee shop for $250,000,with "seller financing," at a 6.0% nominal annual rate.The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years,and then make an additional final (balloon)payment of $50,000 at the end of the last month.What would your equal monthly payments be?
A) $4,029.37
B) $4,241.44
C) $4,464.67
D) $4,699.66
E) $4,947.01

Accepted Answer

The answer of Your cousin will sell you his coffee...

Question 6

Pacific Bank pays a 4.50% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%)does the bank pay?
A) 3.72%
B) 4.13%
C) 4.59%
D) 5.05%
E) 5.56%

Accepted Answer

The formula for effective annual rate (EFF%) is:

EFF% = (1 + (nominal rate/m))^m - 1

where m is the number of compounding periods per year.

In this case, the nominal rate is 4.50% and the compounding is monthly, so:

m = 12 (number of months in a year)
nominal rate/m = 4.50%/12 = 0.375%

EFF% = (1 + 0.00375)^12 - 1 = 4.59%

Therefore, the answer is C, 4.59%.

Question 7

You are considering investing in a bank account that pays a nominal annual rate of 7%,compounded monthly.If you invest $3,000 at the end of each month,how many months will it take for your account to grow to $150,000?
A) 39.60
B) 44.00
C) 48.40
D) 53.24
E) 58.57

Accepted Answer

The answer of You are considering investing in a bank...

Question 8

Partners Bank offers to lend you $50,000 at a nominal rate of 5.0%,simple interest,with interest paid quarterly.An offer to lend you the $50,000 also comes from Community Bank,but it will charge 6.0%,simple interest,with interest paid at the end of the year.What's the difference in the effective annual rates charged by the two banks?
A) 1.56%
B) 1.30%
C) 1.09%
D) 0.91%
E) 0.72%

Accepted Answer

The answer of Partners Bank offers to lend you $50,000...

Question 9

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?
A) $7,531
B) $7,927
C) $8,323
D) $8,740
E) $9,177

Accepted Answer

To calculate the interest paid in Year 2, we need to first calculate the amount of principal that is being paid down in Year 1.

The total amount of interest paid in Year 1 can be found using the formula:

Interest paid in Year 1 = Beginning balance × Interest rate

where Beginning balance = Total loan amount / Number of payments = $100,000 / 10 = $10,000.

So, the interest paid in Year 1 is:

Interest paid in Year 1 = $10,000 × 8.5% = $850.

The total amount of the first payment is the sum of the interest paid in Year 1 and the amount of principal paid down in Year 1:

First payment = Interest paid in Year 1 + Principal paid down in Year 1

The amount of principal paid down in Year 1 can be found using the following formula:

Principal paid down in Year 1 = A - (Beginning balance × Interest rate)

where A is the amount of the first payment, and the Beginning balance and Interest rate are as defined above.

We know that the 10 payments must be equal, so A = $12,937.

Therefore:

Principal paid down in Year 1 = $12,937 - ($100,000 / 10 × 8.5%) = $6,937.

Now we can calculate the interest paid in Year 2.

The beginning balance in Year 2 is:

Beginning balance in Year 2 = Beginning balance - Principal paid down in Year 1

= $100,000 / 10 - $6,937 = $3,063.

So, the interest paid in Year 2 is:

Interest paid in Year 2 = $3,063 × 8.5% = $260.

Therefore, the answer is B) $7,927.

Question 10

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years.How much interest would you have to pay in the first year?
A) $1,200.33
B) $1,263.50
C) $1,330.00
D) $1,400.00
E) $1,470.00

Accepted Answer

The interest for the first year is calculated simply as 10% of the initial loan amount, which is 10% of $14,000 = $1,400.

Question 11

Your older brother turned 35 today,and he is planning to save $7,000 per year for retirement,with the first deposit to be made one year from today.He will invest in a mutual fund that's expected to provide a return of 7.5% per year.He plans to retire 30 years from today,when he turns 65,and he expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.
A) $58,601
B) $61,686
C) $64,932
D) $68,179
E) $71,588

Accepted Answer

To calculate the amount that your brother can spend each year after he retires, we first need to calculate the value of his retirement fund when he retires.

Using the future value formula, we can calculate that the value of his retirement fund when he retires will be:

PV = 0 (since there is no initial investment)
PMT = $7,000
i = 7.5% per year
n = 29 years (since he will make his first deposit one year from today, and retire 30 years from today)

FV = PMT * (((1 + i)^n - 1) / i) = $458,802.93

Next, we need to calculate the amount that he can withdraw each year during retirement, assuming he wants his retirement fund to last for 25 years.

Using the annuity formula, we can calculate that the amount that he can withdraw each year during retirement will be:

PV = $458,802.93
i = 7.5% per year
n = 25 years

PMT = PV * (i / (1 - (1 + i)^(-n))) = $36,837.54

Therefore, he can spend $36,837.54 each year after he retires.

The closest choice is C) $64,932, which is rounded up.

Question 12

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?
A) 15.27%
B) 16.08%
C) 16.88%
D) 17.72%
E) 18.61%

Accepted Answer

When interest is compounded monthly, we need to use the formula for effective annual rate:

(1 + i/m)^m - 1

where i is the nominal annual rate and m is the number of compounding periods per year (in this case, m = 12).

Plugging in the numbers, we get:

(1 + 0.15/12)^12 - 1 = 0.1608, or 16.08%

Therefore, the effective annual rate is 16.08%.

Question 13

Suppose you are buying your first home for $145,000,and you have $15,000 for your down payment.You have arranged to finance the remainder with a 30-year,monthly payment,amortized mortgage at a 6.5% nominal interest rate,with the first payment due in one month.What will your monthly payments be?
A) $741.57
B) $780.60
C) $821.69
D) $862.77
E) $905.91

Accepted Answer

The answer of Suppose you are buying your first home...

Question 14

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.How much would you still owe at the end of the first year,after you have made the first payment?
A) $10,155.68
B) $10,690.19
C) $11,252.83
D) $11,845.09
E) $12,468.51

Accepted Answer

The answer of Suppose you borrowed $15,000 at a rate...

Question 15

The store where you bought new home furnishings offers you two alternative payment plans.The first plan requires a $4,000 immediate up-front payment.The second plan requires you to make monthly payments of $137.41,payable at the end of each month for 3 years.What nominal annual interest rate is built into the monthly payment plan?
A) 12.31%
B) 12.96%
C) 13.64%
D) 14.36%
E) 15.08%

Accepted Answer

The answer of The store where you bought new home...

Question 16

Your Green Investment Tips subscription is about to expire.You plan to subscribe to the magazine for the rest of your life,and you can renew it by paying $85 annually,beginning immediately,or you can get a lifetime subscription for $850,also payable immediately.Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant,how many years must you live to make the lifetime subscription the better buy?
A) 7.48
B) 8.80
C) 10.35
D) 12.18
E) 14.33

Accepted Answer

The answer of Your Green Investment Tips subscription is about...

Question 17

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.By how much would you reduce the amount you owe in the first year?
A) $2,404.91
B) $2,531.49
C) $2,658.06
D) $2,790.96
E) $2,930.51

Accepted Answer

To calculate the amount of each installment, we can use the formula:
Installment = Loan amount / present value annuity factor
where present value annuity factor can be found from a present value of an ordinary annuity table.

Using this formula, we can calculate that each installment will be $3,548.25.

To find out how much of this installment goes towards reducing the amount owed, we can use the formula for the interest in the first year:
Interest = Loan amount * rate
Interest = $15,000 * 8.5%
Interest = $1,275

Therefore, the amount that goes towards reducing the amount owed in the first year is:
Installment - Interest = $3,548.25 - $1,275
= $2,273.25

To check, we can calculate the remaining amount owed after the first year:
Remaining amount owed = Loan amount - (installment - interest)
Remaining amount owed = $15,000 - ($3,548.25 - $1,275)
Remaining amount owed = $12,726.75

We can repeat this process for each of the remaining years, using the remaining amount owed after each year as the starting loan amount.

Using this method, we find that the amount by which the loan amount is reduced in the first year is closest to $2,531.49 (choice B).

Question 18

You are considering investing in a European bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months would it take for your account to grow to $250,000? Round fractional months up.
A) 23
B) 27
C) 32
D) 38
E) 44

Accepted Answer

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

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

Where:
PMT = $5,000
r = 18% = 0.18
n = 12 (monthly compounding)
FV = $250,000

Plugging these values into the formula gives:

$250,000 = $5,000[((1 + 0.18/12)^(12*t) - 1)/(0.18/12)]

Simplifying:

50 = (1.005^(12t) - 1)/0.015

750 = 1.005^(12t) - 1

1.005^(12t) = 751

12t = log(751)/log(1.005)

t = (log(751)/log(1.005))/12

t ≈ 37.9

Rounding up to the nearest integer gives a final answer of 38 months.

Question 19

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month,you will have $13,000 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning? A) 7.62% B) 8.00% C) 8.40% D) 8.82% E) 9.26%

Accepted Answer

The answer of You agree to make 24 deposits of...

Question 20

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate,compounded quarterly.If you also add another $5,000 to the account one year (4 quarters)from now and another $7,500 to the account two years (8 quarters)from now,how much will be in the account three years (12 quarters)from now?
A) $15,234.08
B) $16,035.88
C) $16,837.67
D) $17,679.55
E) $18,563.53

Accepted Answer

To find the total amount in the account three years from now, we need to calculate the future value of each deposit separately, considering the compound interest formula: $A = P(1 + \frac{r}{n})^{nt}$, where:- $A$ is the amount of money accumulated after n years, including interest.- $P$ is the principal amount (the initial amount of money).- $r$ is the annual interest rate (decimal).- $n$ is the number of times that interest is compounded per year.- $t$ is the time the money is invested for in years.1. For the initial $2,500 deposited, it will compound for 3 years (12 quarters):$$A_1 = 2500(1 + \frac{0.04}{4})^{4*3} = 2500(1 + 0.01)^{12} = 2500(1.01)^{12}$$2. For the $5,000 added after 1 year, it will compound for 2 years (8 quarters):$$A_2 = 5000(1 + \frac{0.04}{4})^{4*2} = 5000(1 + 0.01)^{8} = 5000(1.01)^{8}$$3. For the $7,500 added after 2 years, it will compound for 1 year (4 quarters):$$A_3 = 7500(1 + \frac{0.04}{4})^{4*1} = 7500(1 + 0.01)^{4} = 7500(1.01)^{4}$$Calculating each:- $A_1 = 2500(1.01)^{12} ≈ 2816.89$- $A_2 = 5000(1.01)^{8} ≈ 5418.99$- $A_3 = 7500(1.01)^{4} ≈ 7800$Adding them together:$$Total = A_1 + A_2 + A_3 ≈ 2816.89 + 5418.99 + 7800 ≈ 16035.88$$Therefore, the total amount in the account three years from now will be approximately $16,035.88.

Quiz 4: Time Value of Money

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year.How much would be in the account after 8 months,assuming each month has 30 days?

Billy Thornton borrowed $20,000 at a rate of 7.25%,simple interest,with interest paid at the end of each month.The bank uses a 360-day year.How much interest would Billy have to pay in a 30-day month?

You plan to borrow $35,000 at a 7.5% annual interest rate.The terms require you to amortize the loan with 7 equal end-of-year payments.How much interest would you be paying in Year 2?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years.How large would your payments be?

Pacific Bank pays a 4.50% nominal rate on deposits,with monthly compounding.What effective annual rate (EFF%) does the bank pay?

You are considering investing in a bank account that pays a nominal annual rate of 7%,compounded monthly.If you invest $3,000 at the end of each month,how many months will it take for your account to grow to $150,000?

Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business.The terms require you to amortize the loan with 10 equal end-of-year payments.How much interest would you be paying in Year 2?

Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years.How much interest would you have to pay in the first year?

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate,but you must make monthly payments,which amounts to monthly compounding.What is the effective annual rate?

Suppose you are buying your first home for $145,000,and you have $15,000 for your down payment.You have arranged to finance the remainder with a 30-year,monthly payment,amortized mortgage at a 6.5% nominal interest rate,with the first payment due in one month.What will your monthly payments be?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.How much would you still owe at the end of the first year,after you have made the first payment?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years.By how much would you reduce the amount you owe in the first year?

You are considering investing in a European bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months would it take for your account to grow to $250,000? Round fractional months up.

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24^th month,you will have $13,000 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?