Question 1

Consider a deposit of $50,000 that can be made into one of four banks. Which of the following provides the largest balance by the end of five years?
A) Bank A: 8.0% compounded continuously
B) Bank B: 8.0% compounded monthly
C) Bank C: 8.2% compounded annually
D) Bank D: 8.2% simple interest

Accepted Answer

The formula for continuous compounding is $A = P e^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $t$ is the time in years, and $e$ is the base of the natural logarithm (approximately 2.71828). Continuous compounding yields the highest amount due to the constant application of interest, making Bank A the best option despite the same nominal rate as Bank B and a slightly lower rate than Banks C and D.

Question 2

A twenty year-old college student decides to forgo coffee at Starbucks and instead invest the saved $600 per year into a mutual fund earning 6% compounding annually. The amount he would have in the fund by age 65 is closest to:
A) $30,696.07
B) $315,515.24
C) $1,798,973.08

Accepted Answer

Using the formula for future value of an annuity, $FV = P \times \frac{(1 + r)^n - 1}{r}$, where P = $600, r = 0.06 (6%), and n = 45 years (65 - 20), the calculation gives a value closest to $315,515.24. This formula accounts for annual investments at a fixed interest rate compounded annually.

Question 3

A couple nearing retirement plans to increase their retirement savings by investing an equal amount of $20,000 in Roth IRAs each year end, beginning this year. The expected return on the IRAs is 7%. They plan to invest for 10 years. The amount the couple expects to have at the end of ten years is closest to:
A) $39,343.03.
B) $189,743.42.
C) $276,328.96.

Accepted Answer

The couple is making an annual investment of $20,000 at the end of each year for 10 years with an expected return of 7%. This is a case of calculating the future value of an annuity. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of periods. Plugging in the values: FV = $20,000 * [((1 + 0.07)^10 - 1) / 0.07] ≈ $20,000 * 13.4867 ≈ $189,743.42.

Question 4

Caroline's roof is aging. To plan for the eventual roof replacement, she puts $1,000 at the end of each year, starting with this year, into a certificate of deposit (CD) paying 4%. Caroline plans to do this for seven years. The amount Caroline should have at the end of seven years for roof replacement is closest to:
A) $1,315.93
B) $6,002.05
C) $7,898.29

Accepted Answer

Caroline is making an annual investment of $1,000 into a CD that pays 4% interest, compounded annually, for seven years. This is a case of calculating the future value of an annuity, where regular, equal payments are made into an investment that grows at a certain rate. The formula for the future value of an annuity is FV = P * [((1 + r)^n - 1) / r], where P is the payment amount, r is the annual interest rate, and n is the number of periods. Plugging in Caroline's numbers: FV = $1,000 * [((1 + 0.04)^7 - 1) / 0.04], which calculates to approximately $7,898.29.

Question 5

Javier starts a college savings account for his child and places $500 into it every year end, beginning this year. His expected annual return on the account is 2%. He plans to invest for twelve years and then turn over the money to the child for college. The amount he expects to have at the end of the twelve years is closest to:
A) $6,000.00.
B) $6,120.00.
C) $6,706.04.

Accepted Answer

Javier's investment is an example of an ordinary annuity, where payments are made at the end of each period. The future value of an ordinary annuity can be calculated using the formula: FV = P * [(1 + r)^n - 1] / r, where P is the payment amount, r is the annual interest rate, and n is the number of periods. Plugging in the values: P = $500, r = 0.02 (2% expressed as a decimal), and n = 12, we get FV = $500 * [(1 + 0.02)^12 - 1] / 0.02 ≈ $6,706.04.

Question 6

The process of determining how much of each payment is interest and principal repayment best describes the following:
A) mortgage.
B) amortization.
C) present value.
D) balloon payment.

Accepted Answer

Amortization is the process of spreading the cost of a loan over the life of the loan, with each payment consisting of both interest and principal repayment.

Question 7

After making their mortgage payment, the Browns wonder how much their loan balance was reduced by the payment they just made. They should consult a(n):
A) mortgage.
B) amortization schedule.
C) balloon payment schedule.
D) lump sum payment schedule.

Accepted Answer

An amortization schedule provides a detailed breakdown of each mortgage payment, showing how much goes towards the principal balance and how much goes towards interest, thereby indicating how the loan balance is reduced over time.

Question 8

Consider a 5% loan of $150,000 for thirty years, with monthly payments and a balloon payment of $50,000 at the end of thirty years. The monthly payment on this loan is closest to:
A) $599.55
B) $849.55
C) $899.33
D) $1,149.33

Accepted Answer

The answer of Consider a 5% loan of $150,000 for...

Question 9

Consider an 8% loan of $300,000 for twenty years, with monthly payments and a balloon payment of $100,000 at the end of twenty years. The monthly payment on this loan is closest to:
A) $10,714.72
B) $11,381.39
C) $16,072.09
D) $16,738.75

Accepted Answer

The monthly payment on a loan like this can be calculated using the formula for an amortizing loan, but with adjustments for the balloon payment. The loan amount minus the present value of the balloon payment is used to calculate the monthly payments. The present value of the $100,000 balloon payment, using the 8% annual rate converted to a monthly rate (0.08/12), over 240 months (20 years), is subtracted from the initial loan amount to find the amount to be amortized over the loan period. The formula for the monthly payment (PMT) on an amortized loan is PMT = P[r(1+r)^n]/[(1+r)^n - 1], where P is the principal amount (adjusted for the balloon payment), r is the monthly interest rate, and n is the total number of payments. The calculation results in a monthly payment closest to $11,381.39, taking into account the reduced principal due to the future balloon payment.

Question 10

Consider a mortgage of $175,000 that is to be repaid over 360 months. If the annual percentage rate on this mortgage is 4%, the monthly mortgage payments are closest to:
A) $252.14
B) $583.33
C) $835.48
D) $7,000.00

Accepted Answer

The monthly mortgage payment can be calculated using the formula for a fixed-rate mortgage, which is P = [r*PV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate divided by 12), PV is the present value or loan amount ($175,000), and n is the total number of payments (360). With an annual interest rate of 4%, the monthly interest rate is 4%/12 = 0.003333. Plugging these values into the formula gives a monthly payment of approximately $835.48.

Question 11

Consider a mortgage loan of $300,000, to be amortized over thirty years with monthly payments. If the annual percentage rate on this mortgage is 4%, the amount of principal and interest in the second month's mortgage payment is closest to:
A) Principal repayment is $1,000.00, and interest paid is $432.25.
B) Principal repayment is $432.25, and interest paid is $1,000.00.
C) Principal repayment is $998.56, and interest paid is $433.69.
D) Principal repayment is $433.69, and interest paid is $998.56.

Accepted Answer

The monthly interest rate is 0.3333% (4% annual rate divided by 12 months). The first month's interest is $1,000 ($300,000 * 0.3333%). The monthly payment is approximately $1,432.25. In the second month, the interest is calculated on the remaining principal, leading to a principal repayment of $433.69 and interest of $998.56.

Question 12

Vincent would like to have $50,000 per year to live off in his retirement. He expects to retire on his 65^th birthday, make his first retirement withdrawal on his 66^th birthday, and to live until his 85^th birthday. He is celebrating his 30^th birthday today and will make his first savings deposit one year from today. If he can earn 4% per year on his savings, the amount he must save each year to meet his goal, with the last savings deposit on his 65^th birthday, is closest to: A) $7,257.59. B) $7,547.90. C) $7,849.81.

Accepted Answer

To solve this, we use the formula for the future value of an annuity to calculate the amount needed at retirement to withdraw $50,000 annually for 20 years (from age 66 to 85) at a 4% interest rate. Then, we use the formula for the present value of an annuity to determine how much Vincent needs to save annually from age 31 to 65 (35 years) to reach that amount.1. Calculate the future value needed at retirement:$$PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)$$$$50,000 \times \left( \frac{1 - (1 + 0.04)^{-20}}{0.04} \right) = 50,000 \times 14.5949 = 729,745$$2. Calculate the annual savings required:$$PMT = FV \times \left( \frac{r}{1 - (1 + r)^{-n}} \right)$$$$729,745 \times \left( \frac{0.04}{1 - (1 + 0.04)^{-35}} \right) \approx 7,547.90$$Therefore, Vincent needs to save approximately $7,547.90 annually to meet his retirement goal.

Question 13

Discounting is the mathematical conversion of a present value into a future value.

Accepted Answer

The answer of Discounting is the mathematical conversion of a...

Question 14

If the interest rate is equal to 0%, the present value of an amount is equal to the future value of that amount.

Accepted Answer

When the interest rate is 0%, there is no interest earned or paid, so the present value of an amount is exactly equal to its future value, as there is no discounting or compounding effect.

Question 15

The difference between future value with compound interest and future value with simple interest is interest-on -interest.

Accepted Answer

The difference arises because compound interest earns interest on both the initial principal and the interest that has been added to it (interest-on-interest), while simple interest earns interest only on the initial principal.

Question 16

If you know the present value of an investment is $5,000 and the interest rate is 5%, you can calculate future value?

Accepted Answer

The answer of If you know the present value of...

Question 17

A seasoned investor wants to triple her investment in twenty years. To accomplish her objectives, she will have to earn 3.526% on her investment.

Accepted Answer

To triple an investment in 20 years, the investor would need to use the Rule of 72, which estimates the number of years required to double an investment. To triple, it's more complex, but a rough estimate can be made. Doubling would require a 72/20 = 3.6% return approximately for each doubling period. To triple, a higher rate is needed because the investment needs to more than double (actually grow by 200%). The exact rate for tripling can be calculated using the formula for compound interest, which is not 3.526%.

Question 18

Future values represent a special type of cash flow stream that involve equal payments at the same interval, with the same interest rate being applied throughout the period.

Accepted Answer

Future values can refer to the value of any single amount or series of cash flows projected forward in time with interest compounding, not exclusively to equal payments or the same interest rate throughout the period.

Question 19

An annuity that provides periodic payments forever would best be described as a perpetuity.

Accepted Answer

A perpetuity is a type of annuity that provides periodic payments for an infinite amount of time, essentially forever.

Question 20

If each periodic cash flow is the same amount, occurring at the same intervals of time, the present value of a perpetuity will be greater than the present value of a 100-year ordinary annuity.

Accepted Answer

The present value of a perpetuity is calculated as the cash flow divided by the discount rate, and it continues indefinitely. In contrast, a 100-year ordinary annuity has a finite number of cash flows, so its present value will be less than that of a perpetuity, assuming the same cash flow and discount rate.

Quiz 5: Time Value of Money

Consider a deposit of $50,000 that can be made into one of four banks. Which of the following provides the largest balance by the end of five years?

A twenty year-old college student decides to forgo coffee at Starbucks and instead invest the saved $600 per year into a mutual fund earning 6% compounding annually. The amount he would have in the fund by age 65 is closest to:

The process of determining how much of each payment is interest and principal repayment best describes the following:

After making their mortgage payment, the Browns wonder how much their loan balance was reduced by the payment they just made. They should consult a(n) :

Consider a 5% loan of $150,000 for thirty years, with monthly payments and a balloon payment of $50,000 at the end of thirty years. The monthly payment on this loan is closest to:

Consider an 8% loan of $300,000 for twenty years, with monthly payments and a balloon payment of $100,000 at the end of twenty years. The monthly payment on this loan is closest to:

Consider a mortgage of $175,000 that is to be repaid over 360 months. If the annual percentage rate on this mortgage is 4%, the monthly mortgage payments are closest to:

Consider a mortgage loan of $300,000, to be amortized over thirty years with monthly payments. If the annual percentage rate on this mortgage is 4%, the amount of principal and interest in the second month's mortgage payment is closest to: