Question 1

You invested $2,000 in the stock market one year ago. Today, the investment is valued at $9,500. What return did you earn? What return would you need to suffer next year for your investment to be valued at the original $2,000?

Accepted Answer

The return earned in the first year is calculated as (($9,500 - $2,000) / $2,000) * 100 = 375%. To return to the original value of $2,000 from $9,500, the investment would need to lose 78.95% of its value, calculated as (($2,000 - $9,500) / $9,500) * 100.

Question 2

You invested $1,400 in the stock market one year ago. Today the investment is valued at $1,100. What return did you earn? What return would you need to get back next year to break even overall?

Accepted Answer

The return earned is calculated as: (1100 - 1400) / 1400 = -21.43%. To break even, you need to recover the loss, so the required return is: (1400 - 1100) / 1100 = 27.27%.

Question 3

What annual rate of return is earned on an $895 investment that grows to $1,976 in eight years?

Accepted Answer

The annual rate of return can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = \left(\frac{A}{P}\right)^{\frac{1}{n}} - 1$. Plugging in the given values: $A = 1976$, $P = 895$, and $n = 8$, we get $r = \left(\frac{1976}{895}\right)^{\frac{1}{8}} - 1$, which calculates to approximately 10.41 percent.

Question 4

Ten years ago, Hailey invested $1,000 and locked in a 9 percent annual rate for 30 years (end 20 years from now). Aidan can make a 20-year investment today and lock in an 8 percent rate. How much money should he invest now in order to have the same amount of money in 20 years as Hailey?

Accepted Answer

Hailey's investment will grow to $1,000 * (1 + 0.09)^30 in 30 years. To find the equivalent investment for Aidan, solve for the present value using the formula: Future Value = Present Value * (1 + 0.08)^20. Solving gives Aidan's required investment as $2,846.56.

Question 5

What is the value in year 2 of a $200 cash flow made in year 8 if interest rates are 3 percent?

Accepted Answer

The answer of What is the value in year 2...

Question 6

Compute the present value of $4,000 paid in five years using the following discount rates: 10 percent in year 1, 2 percent in year 2, 12 percent in year 3, and 9 percent in years 4 and 5.

Accepted Answer

The correct answer is A because the present value of $4,000 paid in five years using the given discount rates is $2,679.15.

Question 7

Approximately how many years does it take to double a $475 investment when interest rates are 8 percent per year?

Accepted Answer

The answer of Approximately how many years does it take...

Question 8

Scenario A: At age 27, you invest $1,500 that earns 9 percent each year. Scenario B: At age 40, you invest $2,500 that earns 11 percent per year. Under which scenario do you accumulate more money by age 60?

Accepted Answer

In Scenario A, the investment grows for 33 years at 9%, while in Scenario B, it grows for 20 years at 11%. Despite the higher interest rate in Scenario B, the longer time frame and compound interest in Scenario A result in a larger final amount.

Question 9

Approximately what rate is needed to double an investment over five years?

Accepted Answer

Using the Rule of 72, which is a simplified way to estimate the number of years required to double the investment at a fixed annual rate of interest, you divide 72 by the number of years (5) to get approximately 14.4 percent.

Question 10

Scenario A: At age 19 you invest $1,500 that earns 8 percent per year. Scenario B: At age 30 you invest $1,500 that earns 13 percent per year. Under which scenario would you have more money at age 55 and what is the dollar difference at age 55 between the two scenarios?

Accepted Answer

Scenario B earns a higher interest rate, so it will have more money at age 55. The dollar difference between the two scenarios is $7,893.55.

Question 11

How many years (and months) will it take $1 million to grow to $3 million with an annual interest rate of 7.5 percent?

Accepted Answer

The correct answer is A because it takes 15 years and 2.29 months for $1 million to grow to $3 million with an annual interest rate of 7.5 percent.

Question 12

Which is more valuable, receiving $775 today or receiving $885 in 2.5 years if interest rates are 7.25 percent?

Accepted Answer

To determine which option is more valuable, we need to calculate the present value of receiving $885 in 2.5 years at an interest rate of 7.25%. The formula for present value is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($885), r is the interest rate (7.25% or 0.0725), and n is the number of periods (2.5 years). Plugging in the values, we get PV = $885 / (1 + 0.0725)^2.5. This calculation results in a present value of less than $775, making receiving $775 today the more valuable option.

Question 13

What annual rate of return is earned on a $13,000 investment made in year 2 when it grows to $17,000 by the end of year 7?

Accepted Answer

The annual rate of return can be calculated using the formula for compound annual growth rate (CAGR): CAGR = [(Ending Value/Beginning Value)^(1/Number of Years)] - 1. Plugging in the values: CAGR = [(17000/13000)^(1/5)] - 1 = 0.0551 or 5.51 percent.

Question 14

What is the value in year 3 of a $10,000 cash flow made in year 20 if interest rates are 5 percent?

Accepted Answer

To find the value in year 3 of a $10,000 cash flow made in year 20 when interest rates are 5 percent, we need to discount the cash flow back 17 years (from year 20 to year 3). The formula for the present value of a future cash flow is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. Plugging in the values, we get PV = $10,000 / (1 + 0.05)^17, which equals approximately $4,362.97.

Question 15

A stock investor deposited $3,450 six years ago. Today the account is valued at $2,180. What annual rate of return has this investor earned?

Accepted Answer

The answer of A stock investor deposited $3,450 six years...

Question 16

What annual rate of return is implied on a $5,000 loan taken next year when $7,700 must be repaid in year 8?

Accepted Answer

The implied annual rate of return can be calculated using the formula for the future value of a single sum: FV = PV(1 + r)^n, where FV is the future value ($7,700), PV is the present value ($5,000), r is the rate of return, and n is the number of periods (7 years, since the loan is taken next year and repaid in year 8). Rearranging the formula to solve for r gives us r = (FV/PV)^(1/n) - 1. Plugging in the values gives us r = ($7,700/$5,000)^(1/7) - 1 ≈ 0.0636 or 6.36%.

Question 17

Determine the interest rate earned on an $800 deposit when $808 is paid back in one year.

Accepted Answer

The interest earned is $808 - $800 = $8. The interest rate is ($8 / $800) * 100% = 1%.

Question 18

You just won the lottery and after taxes you have $32,000. You want to have $1,000,000 by the time you are 65, which is 45 years from now. Assuming that you can earn 9 percent each year on your money, how much (in dollars) of the $32,000 must you invest today?

Accepted Answer

The answer of You just won the lottery and after...

Question 19

What would be more valuable, receiving $1,895 today or receiving $3,450 in six years if interest rates are 8 percent?

Accepted Answer

The future value of $1,895 in six years at 8% interest is $2,673.44, which is less than $3,450. Therefore, receiving $3,450 in six years would be more valuable.

Question 20

How many years (and months) will it take $4 million to grow to $7 million with an annual interest rate of 12 percent?

Accepted Answer

The answer of How many years (and months) will it...

Quiz 4: Time Value of Money 1: Analyzing Single Cash Flows