Question 1

Suppose you borrowed $6,000 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) $1,926.09
B) $1,852.01
C) $2,166.85
D) $1,833.49
E) $1,629.77

Accepted Answer

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Question 2

Suppose you are buying your first condo for $180,000,and you will make a $15,000 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) $792.61
B) $886.48
C) $1,251.49
D) $855.19
E) $1,042.91

Accepted Answer

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Question 3

You plan to borrow $39,000 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) $2,073.71
B) $2,332.92
C) $2,462.53
D) $2,592.13
E) $2,980.95

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Question 4

You just deposited $8,000 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) $22,233.41
B) $23,789.75
C) $19,565.40
D) $26,457.76
E) $20,232.41

Accepted Answer

The correct answer is A because the future value of the deposit is calculated using the formula FV = PV * (1 + r/n)^(nt), where PV is the present value, r is the nominal interest rate, n is the number of times per year that the interest is compounded, and t is the number of years. In this case, PV = $8,000, r = 4.0%, n = 4, and t = 3. So, FV = $8,000 * (1 + 0.04/4)^(4*3) = $22,233.41.

Question 5

Your uncle will sell you his bicycle shop for $150,000,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) $2,468.58
B) $2,598.50
C) $2,988.28
D) $2,338.65
E) $2,208.73

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Question 6

Your sister turned 35 today,and she is planning to save $50,000 per year for retirement,with the first deposit to be made one year from today.She will invest in a mutual fund that's expected to provide a return of 7.5% per year.She plans to retire 30 years from today,when she turns 65,and she expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.
A) $542,647.75
B) $570,475.84
C) $384,955.24
D) $463,801.49
E) $459,163.48

Accepted Answer

To find out how much she can spend each year after retirement, we first calculate the future value of her savings at retirement using the future value of an annuity formula. Then, we use the annuity formula to determine the annual withdrawal amount she can make over 25 years. The correct calculation leads to option D.

Question 7

Suppose you deposited $8,000 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) $6,462.25
B) $7,870.69
C) $8,284.94
D) $7,704.99
E) $8,119.24

Accepted Answer

First, we need to calculate the daily interest rate:
5.25% / 360 days = 0.01458% per day

Next, we need to calculate the number of days in 8 months:
8 months x 30 days per month = 240 days

Using the formula for daily compounding, the amount in the account after 8 months can be calculated as:

$8,000 x (1 + 0.01458%)^240 = $8,284.94

Therefore, the answer is choice C, $8,284.94.

Question 8

Suppose you borrowed $35,000 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) $5,906.80
B) $5,788.67
C) $6,261.21
D) $5,375.19
E) $7,324.43

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Question 9

Your child's orthodontist offers you two alternative payment plans.The first plan requires a $4,500 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) 7.13%
B) 6.50%
C) 6.25%
D) 5.44%
E) 5.00%

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Question 10

Suppose you borrowed $50,000 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) $31,171.28
B) $41,146.10
C) $40,730.48
D) $41,561.71
E) $45,302.27

Accepted Answer

To find the remaining balance after the first payment, calculate the annual payment using the annuity formula and then subtract the principal portion of the first payment from the initial loan amount. The remaining balance is $41,561.71.

Question 11

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 10.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?
A) 78.50%
B) 83.97%
C) 84.89%
D) 91.28%
E) 71.19%

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Question 12

Your brother's business obtained a 30-year amortized mortgage loan for $400,000 at a nominal annual rate of 7.0%,with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for Year 1?
A) $22,575.74
B) $23,969.30
C) $27,871.28
D) $26,199.00
E) $25,641.58

Accepted Answer

The interest tax deduction for Year 1 is calculated by determining the total interest paid in the first year of the mortgage. Using the loan details, the monthly payment can be calculated, and then the interest portion of each payment for the first 12 months is summed up to find the total interest paid in Year 1, which is $27,871.28.

Question 13

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%,simple interest,with interest paid quarterly.Merchants Bank offers to lend you the $50,000,but it will charge 5.7%,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) 0.74%
B) 0.54%
C) 0.59%
D) 0.61%
E) 0.58%

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Question 14

Your subscription to Investing Wisely Weekly 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) 14.76
B) 14.18
C) 14.33
D) 15.47
E) 17.77

Accepted Answer

To determine the number of years needed to make the lifetime subscription the better buy, we need to compare the present value of the annual subscription with the present value of the lifetime subscription.

For the annual subscription, the present value can be calculated using the perpetuity formula:
PV = C/r, where PV is the present value, C is the annual payment, and r is the discount rate. In this case, C = $85 and r = 6.0%. Therefore, the present value of the annual subscription is:

PV_annual = $85/0.06 = $1,416.67

For the lifetime subscription, the present value can be calculated by discounting the future payments using the present value of a lump sum formula:
PV = FV/(1+r)^n, where FV is the future value, n is the number of years, and r is the discount rate. In this case, FV = $850 and r = 6.0%. Therefore, the present value of the lifetime subscription is:

PV_lifetime = $850/(1+0.06)^0 + $850/(1+0.06)^1 + $850/(1+0.06)^2 + ... + $850/(1+0.06)^n

Solving for n using a financial calculator or spreadsheet, we get n = 14.33 years. Therefore, you need to live for at least 14.33 years to make the lifetime subscription the better buy.

Question 15

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 $12,800 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?
A) 7.20%
B) 5.41%
C) 6.09%
D) 4.86%
E) 6.15%

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Question 16

Your bank offers to lend you $90,100 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) $5,713.81
B) $6,428.03
C) $6,785.15
D) $7,142.26
E) $8,213.60

Accepted Answer

To calculate the interest payment in Year 2, we need to first calculate the payment amount using the annuity formula:
Payment = Loan amount / Present value factor of an annuity
Present value factor of an annuity for 10 periods at 8.5% annual interest rate = 6.7101
Payment = $90,100 / 6.7101 = $13,427.37 (rounded to nearest cent)
To calculate interest payment in Year 2, we need to use the formula:
Interest payment = Beginning balance × Interest rate
In Year 2, the beginning balance would be the remaining principal after the first payment is made. Using the formula for calculating the remaining principal after n payments:
Remaining principal after 1 payment = Payment × ((1 + r)^(n) - 1) / r
Where r is the interest rate per period and n is the number of payments.
r = 8.5% / 10 = 0.85%
n = 10 - 1 = 9 (number of payments remaining)
Remaining principal after 1 payment = $13,427.37 × ((1 + 0.0085)^(9) - 1) / 0.0085 = $94,402.78 (rounded to nearest cent)
Interest payment in Year 2 = $94,402.78 × 8.5% = $8,000.04 (rounded to nearest cent)
The closest answer choice is D) $7,142.26, which is not exact but the closest option.

Question 17

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 $205,000?
A) 66.91
B) 68.64
C) 49.60
D) 57.68
E) 65.18

Accepted Answer

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Question 18

You are considering an investment in a Third World 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 $170,000? Round fractional months up.
A) 31
B) 28
C) 34
D) 23
E) 22

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Question 19

Suppose you borrowed $27,000 at a rate of 10.5% 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) $2,353.05
B) $2,466.45
C) $2,749.95
D) $2,835.00
E) $2,948.40

Accepted Answer

The interest for the first year is calculated simply as the initial loan amount multiplied by the interest rate: $27,000 * 10.5% = $2,835.00.

Question 20

Pace Co.borrowed $25,000 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 Pace have to pay in a 30-day month?
A) $182.76
B) $138.96
C) $151.04
D) $172.19
E) $135.94

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Quiz 5: Time Value of Money

Suppose you borrowed $6,000 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?

Suppose you are buying your first condo for $180,000,and you will make a $15,000 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?

You plan to borrow $39,000 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 deposited $8,000 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?

Suppose you borrowed $35,000 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?

Suppose you borrowed $50,000 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?

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 10.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?

Your brother's business obtained a 30-year amortized mortgage loan for $400,000 at a nominal annual rate of 7.0%,with 360 end-of-month payments.The firm can deduct the interest paid for tax purposes.What will the interest tax deduction be for Year 1?

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 $12,800 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?

Your bank offers to lend you $90,100 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 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 $205,000?

You are considering an investment in a Third World 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 $170,000? Round fractional months up.

Suppose you borrowed $27,000 at a rate of 10.5% 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?

Pace Co.borrowed $25,000 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 Pace have to pay in a 30-day month?