Question 1

Martha is going to receive $6,000 in two years from Tom. She will receive an additional $4,000 in three years from Tom. She earns 7.15% on her investments. How much is this money from Tom worth to Martha today?

Accepted Answer

To find the present value of the future money Martha will receive from Tom, we use the formula for present value: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the annual interest rate, and $n$ is the number of years until the payment is received.For the $6,000 in two years:$$PV = \frac{6,000}{(1 + 0.0715)^2} = \frac{6,000}{1.0715^2} = \frac{6,000}{1.1482} = 5,223.47$$For the $4,000 in three years:$$PV = \frac{4,000}{(1 + 0.0715)^3} = \frac{4,000}{1.0715^3} = \frac{4,000}{1.2250} = 3,265.31$$Adding these two present values together gives the total present value of the money from Tom:$$5,223.47 + 3,265.31 = 8,488.78$$The closest answer to this calculation is B) $8,477.47. However, it seems there was a slight miscalculation in the final step. The correct process was described, but the final addition or the rounding during steps might have been slightly off. The principle of calculating each payment's present value and then summing them is correct for determining the total present value of future payments.

Question 2

Thirty years ago, your father invested $6,000. Today that investment is worth $67,270.98. What is the average rate of return your father earned on this investment?

Accepted Answer

The average rate of return can be calculated using the formula for compound interest: FV = PV * (1 + r)^n. Solving for r, we get r = (FV/PV)^(1/n) - 1. Plugging in the values: r = ($67,270.98/$6,000)^(1/30) - 1 = 8.39%.

Question 3

The James Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of $15,000 and expects to earn 4% interest. After 3 years, the firm wants to add an additional $50,000 to the account. If the account continues to earn 4%, how much money will the James Co. have in their account five years from now?

Accepted Answer

The answer of The James Co. plans on saving money...

Question 4

Tropical Tans is saving money to build a new salon. Three years ago, they set aside $12,000 for this purpose. Today, that account is worth $16,418. What rate of interest is Tropical Tans earning on this money?

Accepted Answer

The answer of Tropical Tans is saving money to build...

Question 5

Thirty years ago, your father invested $11,000. Today, that investment is worth $287,047.

What is the average annual rate of return your father earned on his investment?

Accepted Answer

The answer of Thirty years ago, your father invested $11,000....

Question 6

The present value interest factor is calculated as:

Accepted Answer

The present value interest factor is calculated using the formula 1/(1 + r)^t, where r is the interest rate and t is the time period.

Question 7

You deposit $500,000 in a higher risk investment. Three years later, you receive $711,900 and withdraw your funds. Given this information calculate the interest earned at the end of year 3.

Accepted Answer

The interest earned is calculated by subtracting the initial investment from the final amount: $711,900 - $500,000 = $211,900.

Question 8

Gretchen Enterprises borrowed $149,500 for two years from the bank. At the end of the two years, they repaid the loan with one payment of $176,590. What was the interest rate on the loan?

Accepted Answer

The correct answer is A because the interest rate on the loan was 8.68%. This can be calculated using the formula: Interest = Principal * Rate * Time, where Principal is the amount of money borrowed, Rate is the interest rate, and Time is the length of time the money is borrowed for. In this case, the Principal is $149,500, the Time is 2 years, and the Interest is $176,590 - $149,500 = $27,090. So, the Rate can be calculated as: Rate = Interest / (Principal * Time) = $27,090 / ($149,500 * 2) = 0.0868, or 8.68%.

Question 9

The future value interest factor is calculated as:

Accepted Answer

The future value interest factor is correctly represented by the formula (1 + r)^t, where "r" represents the interest rate and "t" represents the time period. This formula is used to calculate the future value of an investment or loan based on compound interest.

Question 10

In 1889, Vincent Van Gogh's painting, "Sunflowers," sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, what annual return on investment would your family have earned on the painting?

Accepted Answer

The answer of In 1889, Vincent Van Gogh's painting, "Sunflowers,"...

Question 11

You deposit $3,000 in a retirement account today at 5.5% interest. How much more money will you have if you leave the money invested for forty-five years rather than forty years?

Accepted Answer

The answer of You deposit $3,000 in a retirement account...

Question 12

You deposit $1,000 in a retirement account today at 8.5% interest. How much more money will you have if you leave the money invested for 40 years rather than 35 years?

Accepted Answer

The answer of You deposit $1,000 in a retirement account...

Question 13

What is the future value of $4,160 invested for eight years at 8.5% compounded annually?

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value or initial investment, r is the annual interest rate (in decimal form), and n is the number of years the money is invested for. Plugging in the given values: FV = $4,160(1 + 0.085)^8 = $7,989.71.

Question 14

Lakeside Inc. invested $735,000 at an 11.25% rate of return. The company sold their investment for $1,067,425. How much longer would Lakeside have had to wait if they had wanted to sell their investment for $1.25 million?

Accepted Answer

First, calculate the annual interest earned by the investment: $735,000 * 11.25% = $82,687.50. To find out how much more money is needed to reach $1.25 million from the selling price of $1,067,425, subtract $1,067,425 from $1,250,000, which equals $182,575. Then, divide $182,575 by the annual interest of $82,687.50 to find out how many more years are needed: $182,575 / $82,687.50 = 2.21. Since the question asks for how much longer beyond the initial period, subtract the initial period (0.73 years, calculated from the first profit of $332,425 over $82,687.50 per year) from 2.21 years to get approximately 1.48 years.

Question 15

One year ago, you invested $2,500. Today it is worth $2,789.50. What rate of interest did you earn?

Accepted Answer

The interest earned is $2,789.50 - $2,500 = $289.50. The rate of interest is $289.50 / $2,500 * 100% = 11.58%.

Question 16

Omar has an investment valued at $12,345 today. He made a one-time investment at 6.5% four years ago. Leon has an investment that is also valued at $12,345 today. Leon invested four years ago at 7.5%. Omar originally invested _____ and Leon invested _____.

Accepted Answer

To find the original investment, use the formula for compound interest: P = A / (1 + r)^n. For Omar: P = 12345 / (1 + 0.065)^4 = $9,596.05. For Leon: P = 12345 / (1 + 0.075)^4 = $9,243.94.

Question 17

Today, your grandmother gave you a gift of $25,000 to help pay for your college education. She told you that this amount was the result of a one-time investment at 8% interest 13 years ago. How much did your grandmother originally invest?

Accepted Answer

To find the original investment, use the formula for compound interest: 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. Since the interest is compounded annually (implied by the lack of information to the contrary), n = 1. Given A = $25,000, r = 8% or 0.08, and t = 13 years, we solve for P: $25,000 = P(1 + 0.08/1)^(1*13), which simplifies to $25,000 = P(1.08)^13. Solving for P gives approximately $9,192.45.

Question 18

The Blackwell Co. expects to receive $135,000 from an insurance settlement four years from now. If the company can earn 11% on its investments, what is the value of the insurance settlement worth today?

Accepted Answer

The answer of The Blackwell Co. expects to receive $135,000...

Question 19

The Smith Co. has $450,000 to invest at 5.5% interest. How much more money will they have if they invest these funds for eight years instead of five years?

Accepted Answer

The answer of The Smith Co. has $450,000 to invest...

Question 20

Your grandmother invested one lump sum 42 years ago at 3.5% interest. Today, she gave you the proceeds of that investment which totaled $28,204.37. How much did your grandmother originally invest?

Accepted Answer

The answer of Your grandmother invested one lump sum 42...

Quiz 5: Introduction to Valuation: the Time Value of Money