Question 1

Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?

Accepted Answer

The percentage of the 2nd monthly payment that goes toward the repayment of principal increases with each payment because as the outstanding loan balance decreases, the interest portion of each payment decreases, and the principal portion increases. To calculate this, first, find the monthly interest rate, which is 11.0% / 12 = 0.917%. Then, use the loan formula to find the monthly payment amount. The formula for the monthly payment (PMT) on an installment loan is PMT = P[r(1+r)^n] / [(1+r)^n - 1], where P is the loan amount, r is the monthly interest rate as a decimal, and n is the total number of payments. Substituting the given values (P = $72,500, r = 0.00917, n = 12), we find the monthly payment. Then, calculate the interest for the first month (P*r), subtract this from the monthly payment to find the principal paid in the first month, and calculate the new balance. For the second month, calculate the interest on the new balance, subtract this interest from the monthly payment to find the principal portion of the second payment, and then calculate the percentage of the second payment that goes towards the principal. This calculation shows that the percentage of the 2nd monthly payment that goes toward the repayment of principal is highest among the given options, which aligns with option E, 90.45%.

Question 2

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?

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 3

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed for annuities where the payments occur either at the beginning or the end of the periods. This is because the timing of the payments can affect the present value and future value calculations. As long as the timing of the cash flows is consistent, a time line can be used to visualize the cash flows and calculate their values. Other options are incorrect because cash flows can be uneven, time lines are useful for visualizing problems, and time lines can be constructed for any type of cash flow pattern, not just annual payments.

Question 4

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed where some of the payments are part of an annuity and others are not. This is known as a mixed stream of cash flows. Time lines are a useful tool for visualizing and analyzing complex problems before doing actual calculations. Cash flows can occur annually, quarterly, or at any other frequency. Finally, time lines can be constructed for both ordinary annuities and annuities due, where payments occur at the beginning of the period.

Question 5

Your aunt wants to retire and has $375,000.She expects to live for another 25 years and to earn 7.5% on her invested funds.How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Accepted Answer

The answer of Your aunt wants to retire and has...

Question 6

Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year.How much could you withdraw at the end of each of the next 20 years?

Accepted Answer

The answer of Suppose you earned a $275,000 bonus this...

Question 7

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?

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 8

Your aunt wants to retire and has $375,000.She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds.How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account?

Accepted Answer

To find the annual withdrawal amount, we use the formula for the annuity withdrawal: PMT = PV * [r / (1 - (1 + r)^-n)], where PV = $375,000, r = 7.5% or 0.075, and n = 25 years. Solving this gives approximately $31,294.42.

Question 9

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?

Accepted Answer

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

Question 10

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?

Accepted Answer

To calculate the interest paid in year two, we need to first calculate the annual payment:
PV = $100,000
Annual interest rate = 8.5%
Number of years = 10
Using the formula for calculating an amortization payment, we get:
Annual payment = PV*(r*(1+r)^n) / ((1+r)^n - 1)
= $100,000*(0.085*(1+0.085)^10) / ((1+0.085)^10 - 1)
= $15,735.95
The interest paid in the second year is equal to the outstanding balance at the end of the first year multiplied by the annual interest rate.
Outstanding balance at the end of the first year = PV*(1+r)^(n-1) - annual payment*((1+r)^n - (1+r)^(n-1))/r
= $100,000*(1+0.085)^(1-1) - $15,735.95*((1+0.085)^10 - (1+0.085)^(1-1))/0.085
= $87,064.05
Interest paid in the second year = $87,064.05*0.085 = $7,927.

Question 11

Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate.He now has decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year.What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

Accepted Answer

The answer of Your uncle just won the weekly lottery,...

Question 12

Suppose you inherited $275,000 and invested it at 8.25% per year.How much could you withdraw at the beginning of each of the next 20 years?

Accepted Answer

The answer of Suppose you inherited $275,000 and invested it...

Question 13

Your Aunt Elsa has $500,000 invested at 6.5%, and she plans to retire.She wants to withdraw $40,000 at the beginning of each year, starting immediately.What is the maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the nearest whole number.)

Accepted Answer

The answer of Your Aunt Elsa has $500,000 invested at...

Question 14

Your sister's pet supplies business obtained a 30-year amortized mortgage loan for $250,000 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 for the first year of the loan? (Assume she took out the loan on January 1.)

Accepted Answer

The correct answer is A. The interest tax deduction for the first year of the loan is $17,419.55. This is calculated as follows:Interest paid in first year = $250,000 x 7.0% x 12 / 360 = $5,833.33Interest tax deduction = $5,833.33 x (1 - tax rate) = $5,833.33 x (1 - 0.35) = $3,801.67Total interest tax deduction for first year = $5,833.33 + $3,801.67 = $17,419.55

Question 15

Which of the following statements is CORRECT?

Accepted Answer

Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly. Time lines can also be used for visualizing complex problems and comparing different cash flow scenarios. However, option A is incorrect because time lines can be constructed for situations where some payments are part of an annuity while others are not, and option B is incorrect because time lines can be constructed for any time frame. Option E is also incorrect because time lines can be constructed for annuities with payments at the beginning and end of the period (called annuities due and ordinary annuities, respectively).

Question 16

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?

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 17

Your uncle has $300,000 invested at 7.5%, and he now wants to retire.He wants to withdraw $35,000 at the end of each year, beginning at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

Accepted Answer

This problem can be solved using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (initial investment), PMT is the annual withdrawal amount, r is the annual interest rate, and n is the number of payments. Rearranging to solve for n, and considering the future value that needs to remain ($25,000), we adjust the equation to account for this by subtracting the future value discounted back to the present value from the initial investment. Using trial and error or financial calculators and plugging in the given values ($300,000 initial investment, 7.5% interest rate, $35,000 withdrawal), we find that the maximum number of $35,000 withdrawals that can be made while still leaving at least $25,000 in the account is 13.

Question 18

Which of the following statements is CORRECT?

Accepted Answer

Time lines are very useful for visualizing cash flows and helping with calculations, especially in complex problems. They can be constructed for a variety of cash flow patterns, including annuity payments and uneven amounts. They are not limited to annual cash flows and can be constructed for quarterly or even daily cash flows. Additionally, time lines can be constructed for annuities with payments at the beginning of the periods, although this requires a slight modification to the traditional time line format.

Question 19

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?

Accepted Answer

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

Question 20

You were left $100,000 in a trust fund set up by your grandfather.The fund pays 6.5% interest.You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately.How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

Accepted Answer

The problem involves calculating the annuity payment for a present value of $100,000 at an interest rate of 6.5% over 4 periods. Using the formula for the present value of an annuity, the correct withdrawal amount is $27,409.

Quiz 4: Time Value of Money

Your business has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments.What percentage of the 2nd monthly payment will go toward the repayment of principal?

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?

Which of the following statements is CORRECT?

Which of the following statements is CORRECT?

Your aunt wants to retire and has $375,000.She expects to live for another 25 years and to earn 7.5% on her invested funds.How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Suppose you earned a $275,000 bonus this year and invested it at 8.25% per year.How much could you withdraw at the end of each of the next 20 years?

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?

Your aunt wants to retire and has $375,000.She expects to live for another 25 years, and she also expects to earn 7.5% on her invested funds.How much could she withdraw at the beginning of each of the next 25 years and end up with zero in the account?

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 inherited $275,000 and invested it at 8.25% per year.How much could you withdraw at the beginning of each of the next 20 years?

Which of the following statements is CORRECT?

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?

Which of the following statements is CORRECT?

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?