Question 1

Alexis owns stock in a company which has consistently paid a growing dividend over the last 10 years. The first year Alexis owned the stock, she received $4.50 per share and in the 10th year, she received $4.92 per share. What is the growth rate of the dividends over the last 10 years?

Accepted Answer

The growth rate of the dividends can be calculated using the formula for compound annual growth rate (CAGR), which is $CAGR = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$, where FV is the final value ($4.92), PV is the initial value ($4.50), and n is the number of periods (10 years). Plugging in the values gives a growth rate of approximately 0.9% per year, which over 10 years accumulates to approximately 9.3%, making option D correct.

Question 2

The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years is approximately ________.

Accepted Answer

To find the rate of return earned on an investment, we need to use the present value of an annuity formula.

Present value of an annuity = (payment amount x (1 - (1 + r)^(-n))) / r

Where, 
payment amount = $10,489 
n = 6 years 
r = rate of return

Using a financial calculator or excel solver function, we can solve for the rate of return that equates the present value of the annuity payments with the initial investment of $50,000.

The answer is approximately 7%. Therefore, the best choice is B, 7%.

Question 3

Xiao Li wishes to accumulate $50,000 by the end of 10 years by making equal annual end-of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her investments, how much must she deposit at the end of each year?

Accepted Answer

The future value of an annuity is given by the formula:FV = PMT * [(1 + r)^n - 1] / rwhere:PMT is the annual paymentr is the annual interest raten is the number of yearsIn this case, we have:FV = $50,000r = 5% = 0.05n = 10 yearsSubstituting these values into the formula, we get:$50,000 = PMT * [(1 + 0.05)^10 - 1] / 0.05$50,000 = PMT * 6.475PMT = $50,000 / 6.475PMT = $3,975Therefore, Xiao Li must deposit $3,975 at the end of each year to accumulate $50,000 by the end of 10 years.

Question 4

Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be repaid in four equal annual installments. The interest paid in the first year is ________.

Accepted Answer

The interest paid in the first year is calculated on the initial amount borrowed. Since Aunt Tilly borrows $3,500 at 12 percent annually, the first year's interest is 12% of $3,500, which is $420.

Question 5

Zheng Sen wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years. If Zheng Sen can earn 10 percent on his investments, how much must he deposit at the end of each year?

Accepted Answer

To solve this, we use the formula for the future value of an annuity: FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($1 million), P is the annual payment, r is the annual interest rate (10% or 0.10), and n is the number of periods (20 years). Rearranging the formula to solve for P gives us P = FV / [((1 + r)^n - 1) / r]. Plugging in the numbers: P = $1,000,000 / [((1 + 0.10)^20 - 1) / 0.10] = $17,460 (approximately).

Question 6

What is the rate of return on an investment of $124,090 if the company expects to receive $10,000 per year for the next 30 years?

Accepted Answer

The rate of return is calculated by dividing the annual income by the initial investment. In this case, the annual income is $10,000 and the initial investment is $124,090. Therefore, the rate of return is $10,000/$124,090 = 0.0806, or 8.06%. The closest answer choice is 7%, so the correct answer is A.

Question 7

Otto is planning for his son's college education to begin ten years from today. He estimates the end-of-the-year tuition, books, and living expenses to be $10,000 per year for a four-year degree. How much must Otto deposit today, at an interest rate of 12 percent, for his son to be able to withdraw $10,000 per year for four years of college?

Accepted Answer

The answer of Otto is planning for his son's college...

Question 8

Ashley owns stock in a company which has consistently paid a growing dividend over the last five years. The first year Ashley owned the stock, she received $1.71 per share and in the fifth year, she received $2.89 per share. What is the growth rate of the dividends over the last five years?

Accepted Answer

The growth rate of the dividends can be calculated using the formula for the compound annual growth rate (CAGR), which is $$CAGR = \left(\frac{FV}{PV}\right)^{\frac{1}{n}} - 1$$ where FV is the future value ($2.89), PV is the present value ($1.71), and n is the number of periods (5 years). Plugging in the values gives $$CAGR = \left(\frac{2.89}{1.71}\right)^{\frac{1}{5}} - 1 \approx 0.11$$ or 11 percent.

Question 9

A local bank is offering a zero-coupon certificate of deposit for $25,000. At maturity, three years from now, the investor will receive $32,000. What is the rate of return on this investment?

Accepted Answer

The rate of return can be calculated using the formula:

Rate of return = [(future value/present value)^(1/n)] - 1

where,
future value = $32,000
present value = $25,000
n = 3 (years)

Plugging in the values, we get:

Rate of return = [(32000/25000)^(1/3)] - 1 
               = 0.0843 or 8.43% (approx.)

Therefore, the closest option is C) 9 percent, which is the best choice.

Question 10

Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment, how much must each deposit be in order to accumulate the $40,000?

Accepted Answer

Using the formula for the future value of an annuity:
FV=Pmt[(1+r)^n-1]/r
where
FV= future value
Pmt= periodic payment
r= annual interest rate
n= number of periods

Substituting the given values:
$40,000=Pmt[(1+0.09)^5-1]/0.09

Solving for Pmt:
Pmt=$6,684.18, which is closest to choice B.

Question 11

Julian was given a gold coin originally purchased for $1 by his great-grandfather 50 years ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is approximately equal to ________.

Accepted Answer

The rate of return can be calculated using the formula for compound annual growth rate (CAGR), which is [(Final Value/Initial Value)^(1/Number of Years)] - 1. Plugging in the values: [(450/1)^(1/50)] - 1 ≈ 0.13 or 13%.

Question 12

A ski chalet at Peak n' Peak now costs $250,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 10 years before Chris and Julie retire from successful investment banking careers. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon retirement?

Accepted Answer

The answer of A ski chalet at Peak n' Peak...

Question 13

A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000. At maturity, three years from now, the investor will receive $14,000. What is the rate of return on this investment?

Accepted Answer

The rate of return can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount at maturity ($14,000), $P$ is the principal amount ($10,000), $r$ is the annual rate of return, and $n$ is the number of years (3). Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Substituting the given values, we get $r = \left(\frac{14000}{10000}\right)^{\frac{1}{3}} - 1 = 1.25992 - 1 = 0.12$, or 12 percent.

Question 14

What is the rate of return on an investment of $16,278 if the company expects to receive $3,000 per year for the next 10 years?

Accepted Answer

The formula to calculate the rate of return is (amount received/initial investment)^(1/n) - 1, where n is the number of years. Substituting the given values, we get (3000/16278)^(1/10) - 1 = 0.0128 or 1.28%. Hence, the rate of return is 1.28% per year, which is closest to option B - 13 percent. Therefore, the best choice is B.

Question 15

Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8 percent interest rate. The original principal amount was ________.

Accepted Answer

The answer of Hayley makes annual end-of-year payments of $6,260.96...

Question 16

Thelma is planning for her son's college education to begin five years from today. She estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year degree, assuming th expenses incur only at the end of the year. How much must Thelma deposit today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four years of college?

Accepted Answer

To solve this, we use the present value of an annuity formula, which is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($5,000), r is the annual interest rate (8% or 0.08), and n is the number of periods (4 years). However, since the withdrawals start in 5 years, we also need to discount the result back to today, which is done by dividing by (1 + r)^n, where n in this case is 5 years. The calculation is as follows: PV = $5,000 * [(1 - (1 + 0.08)^-4) / 0.08] = $16,319.48 as the present value of the annuity at the beginning of the college period. To find how much Thelma must deposit today, we discount this amount back 5 years: $16,319.48 / (1 + 0.08)^5 = $11,270.

Question 17

Dorothy borrows $10,000 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $3,223.73. The annual interest rate on the loan is ________.

Accepted Answer

Using the formula for annuity payments, we can solve for the interest rate:

PV = PMT x [(1 - (1+i)^-n)/i], where PV is the present value (borrowed amount), PMT is the annual payment, i is the interest rate, and n is the number of periods (years).

Plugging in the given values, we get:

$10,000 = $3,223.73 x [(1 - (1+i)^-4)/i]

Solving for i through trial and error or using a financial calculator, we get i ≈ 0.1107 or 11.07%.

Therefore, the answer is C) 11 percent.

Question 18

Detta borrows $20,000 from the bank. For a five-year loan, the bank requires annual end-of-year payments of $4,878.05. The annual interest rate on the loan is ________.

Accepted Answer

The correct answer can be found by using the formula for the present value of an annuity, which calculates the original loan amount based on the annual payments, interest rate, and number of periods. By plugging the given values into the formula or using a financial calculator, it can be determined that an interest rate of 7 percent results in a present value (or loan amount) of $20,000 when the annual payments are $4,878.05 for five years.

Question 19

Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was ________.

Accepted Answer

The correct answer is found by calculating the present value of an annuity, which is the original principal amount of the loan. The formula for the present value of an annuity is P = PMT [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the annual interest rate (as a decimal), and n is the number of payments. Using the given annual payment of $5,043.71, an interest rate of 13% (or 0.13 as a decimal), and a total of 4 payments, the calculation yields a present value (original principal) close to $15,000.

Question 20

A beach house in Southern California now costs $350,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from successful careers in commercial art. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the beach house upon retirement?

Accepted Answer

To find the future price of the beach house, calculate $350,000 * (1.05)^20. Then, use the future value of an annuity formula to find the annual deposit needed to reach that future price, given an interest rate of 13%. The correct calculation results in an annual deposit of approximately $11,472.

Quiz 5: Time Value of Money