Question 1

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 2

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

First, we need to calculate the annual payment using the amortization formula:
PMT = r * PV / (1 - (1 + r)^(-n))
where
PMT = annual payment
r = annual interest rate
PV = present value of the loan
n = number of payments

Plugging in the given values:
PMT = 0.075 * 35,000 / (1 - (1 + 0.075)^(-7))
PMT = $6,188.01

In the second year, we need to calculate the interest portion of the second payment. To do this, we first need to find the principal portion of the first payment, which we can do using the formula:
Principal = PMT - r * PV
where
Principal = principal portion of the payment
PMT = payment amount
r = annual interest rate
PV = present value of the loan

Plugging in the given values:
Principal = $6,188.01 - 0.075 * $35,000
Principal = $3,758.51

Since the loan is being amortized, the principal portion of each payment will increase and the interest portion will decrease. In the second year, the principal portion will be higher and the interest portion will be lower than in the first year. To find the interest portion of the second payment, we need to subtract the principal portion of the first payment from the total interest paid over the first two payments:

Total interest paid over first two payments = r * PV + r * (PV - Principal)
Total interest paid over first two payments = 0.075 * $35,000 + 0.075 * ($35,000 - $3,758.51)
Total interest paid over first two payments = $5,371.49

Interest portion of second payment = Total interest paid over first two payments - Interest portion of first payment
Interest portion of second payment = $5,371.49 - ($6,188.01 - $3,758.51)
Interest portion of second payment = $2,326.27

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

Question 3

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 4

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

We can begin by using the formula for simple interest:

I = Prt

where I is the interest, P is the principal, r is the interest rate per period, and t is the time in periods.

In this case, P = $20,000, r = 0.0725 per month (since the annual rate is divided by 12 for monthly payments), and t = 1 (since we want to calculate the interest for one month).

Plugging in these values, we get:

I = ($20,000)(0.0725)(1) = $1,450

However, we need to remember that the bank uses a 360-day year. This means that each month is considered to have 30 days. To find the interest for a 30-day month, we simply divide the annual interest rate by 360 and multiply by 30:

r = 0.0725/360 * 30 = 0.00625

Now we can use the formula again:

I = ($20,000)(0.00625)(1) = $125

Therefore, the answer is A, $120.83, since this is the closest option to $125.

Question 5

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 6

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 7

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

First, we need to calculate the annual payment for the loan using the amortization formula:
Payment = (Loan amount * interest rate) / (1 - (1 + interest rate)^-n)
where n is the number of payments (in this case, 10).

Payment = (100,000 * 0.085) / (1 - (1 + 0.085)^-10) = $15,210.92

Now, we can use this payment amount to calculate the interest paid in Year 2. To do this, we need to calculate the outstanding balance of the loan at the end of Year 1, which will be the beginning balance for Year 2.

Outstanding balance at end of Year 1 = (Present value of remaining payments) / (1 + interest rate)^n
where n is the number of periods remaining (in this case, 9)
Present value of remaining payments = Payment * ((1 - (1 + interest rate)^-n) / interest rate)

Present value of remaining payments = $15,210.92 * ((1 - (1 + 0.085)^-9) / 0.085) = $104,025.39

Outstanding balance at end of Year 1 = $104,025.39 / (1 + 0.085)^9 = $59,696.98

Now we can calculate the interest paid in Year 2, which will be the beginning balance for Year 2 multiplied by the interest rate:

Interest paid in Year 2 = $59,696.98 * 0.085 = $5,072.45

But we also need to add the interest paid in Year 1 to get the total interest paid during the first two years:

Interest paid in Year 1 = $100,000 * 0.085 = $8,500.00

Total interest paid in Years 1 and 2 = $8,500.00 + $5,072.45 = $13,572.45, which is closest to option B: $7,927.

Question 8

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 9

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

Using the formula for calculating the equal installment, we get:

Installment = (Principal x Rate)/(1 - (1+Rate)^-n)

where Principal = $15,000, Rate = 8.5% = 0.085, and n = 5 (for 5 years).

Installment = (15000 x 0.085)/(1 - (1+0.085)^-5) = $3,738.45

This means that you need to pay $3,738.45 at the end of each of the next 5 years.

Now, to calculate how much you would reduce the amount you owe in the first year, we need to use the formula for calculating the interest component of the installment, which is:

Interest = Outstanding principal x Rate

For the first year, the outstanding principal is the original principal amount of $15,000. So, the interest component of the first installment is:

Interest = 15,000 x 0.085 = $1,275

Therefore, the amount by which you would reduce the amount you owe in the first year is:

Reduction = Installment - Interest = $3,738.45 - $1,275 = $2,463.45

Rounding this to the nearest cent gives us the final answer of:

Reduction = $2,531.49 (Option B)

Question 10

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

The answer of Your older brother turned 35 today, and...

Question 11

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

To calculate the effective annual rate (EFF%), we use the formula:
EFF% = (1 + (nominal rate/number of compounding periods))^number of compounding periods - 1
Plugging in the given values, we get:
EFF% = (1 + (0.045/12))^12 - 1
EFF% = 0.0457 or 4.57%
Therefore, the bank pays an effective annual rate of 4.57%. The closest option is C, which is 4.59%.

Question 12

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 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

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 15

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 16

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 17

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.

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 compound interest to solve this problem:

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

where:
A = final amount ($250,000)
P = initial investment per month ($5,000)
r = annual interest rate (18%)
n = number of times interest is compounded per year (12 for monthly)
t = time in years (unknown)

Plugging in the given values, we get:

$250,000 = $5,000(1 + 0.18/12)^(12t)

Simplifying, we get:

50 = (1 + 0.015)^12t

log(50) = 12t*log(1.015)

t = log(50)/(12*log(1.015)) = 37.52

Rounding up to the nearest month, we get:

t = 38

Therefore, it would take 38 months for the account to grow to $250,000. 
The correct answer is D.

Question 19

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 20

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

Since we have monthly compounding, we need to use the effective monthly rate formula and then convert it to the effective annual rate:
Effective monthly rate = (1 + nominal annual rate/12)^12 - 1 = (1 + 0.15/12)^12 - 1 = 1.2625%.
Effective annual rate = (1 + effective monthly rate)^12 - 1 = (1 + 0.012625)^12 - 1 = 16.08%. Therefore, the effective annual rate is 16.08%.

Quiz 4: Time Value of Money

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?

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?

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?

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 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?

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?

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

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?

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

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?

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.

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?

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?