Question 1

Compound interest is best defined as the interest earned:

Accepted Answer

The answer of Compound interest is best defined as the...

Question 2

The amount an investment is worth after one or more periods of time is the ___________.

Accepted Answer

The future value of an investment refers to the amount it is worth after one or more periods of time, taking into account factors like interest rates and compounding periods.

Question 3

Ito invested $4,350. After seven years he had an account value of $6,980.58. Maria invested $5,920. After six years she had an account value of $8,834.62. Which one of the following statements is correct?

Accepted Answer

The answer of Ito invested $4,350. After seven years he...

Question 4

Ten years ago, Joe invested $5,000. Five years ago, Marie invested $2,500. Today, both Joe and Marie's investments are each worth $8,500. Which one of the following statements is correct concerning their investments?

Accepted Answer

The answer of Ten years ago, Joe invested $5,000. Five...

Question 5

Twelve years ago, Jake invested $2,000. Six years ago, Tami invested $4,000. Today, both Jake's and Tami's investments are each worth $9,700. Assume that both Jake and Tami continue to earn their respective rates of return. Which one of the following statements is correct concerning these investments?

Accepted Answer

Tami has earned an average annual interest rate of 15.91%.

Question 6

Twenty years ago, Max invested $10,000. Thirty years ago, Julie invested $5,000. Today, both Max and Julie's investments are each worth $35,000. Which one of the following statements is correct concerning their investments? Assume that they will continue earning the same rate of return.

Accepted Answer

The answer of Twenty years ago, Max invested $10,000. Thirty...

Question 7

The value today of future cash flows discounted at the appropriate discount rate is called the _____ value.

Accepted Answer

The value today of future cash flows discounted at the appropriate discount rate is called the Present value. This concept is a fundamental principle in finance, reflecting the time value of money.

Question 8

Katie is going to receive $1,000 three years from now. Wilt is going to receive $1,000 five years from now. Which one of the following statements is correct if both Katie and Wilt apply a 5% discount rate to these amounts?

Accepted Answer

E) Katie's money is worth more than Wilt's money today because the present value of money decreases with time when applying a discount rate. Since Katie receives her money sooner than Wilt, her $1,000 has a higher present value when discounted back to today's dollars at a 5% rate.

Question 9

The greater the number of years, the:

Accepted Answer

The greater the number of years, the greater the compounding effect, as interest has more time to accumulate on both the initial principal and the accumulated interest from previous periods.

Question 10

All else being the same, which of the following statements is correct?

Accepted Answer

Present values are calculated by discounting future values back to the present using a discount rate (r). When both the discount rate (r) and the time period (t) are positive, the present value will indeed be smaller than the future value. This is because the process of discounting reduces the future value to account for the time value of money.

Question 11

Fred and Max each want to have $10,000 saved five years from now. Fred can earn 4.35%, compounded annually, on his savings and Max can earn 4.50%, compounded annually, on his savings. Both Fred and Max are going to deposit one lump sum today and will not add any additional funds to their accounts. Given this, Max _____ deposit _____ Fred to achieve the goal.

Accepted Answer

Since Max can earn a higher interest rate, he can deposit less than Fred to achieve the same goal of $10,000 in five years.

Question 12

Isaac and Faith both want to have $5,000 in three years. Isaac expects to earn 8% on his investments and Faith expects a 7% rate of return. Which one of the following statements is correct concerning the amount of money they each need to invest today?

Accepted Answer

To find the amount each needs to invest today, we use the formula for the present value of a single sum, which is PV = FV / (1 + r)^n, where PV is the present value (amount needed to invest today), FV is the future value ($5,000), r is the annual interest rate (expressed as a decimal), and n is the number of years. For Isaac, r = 0.08 and for Faith, r = 0.07. Calculating the present value for each: Isaac: PV = $5,000 / (1 + 0.08)^3 ≈ $3,922.61. Faith: PV = $5,000 / (1 + 0.07)^3 ≈ $4,035.24. The difference: $4,035.24 - $3,922.61 ≈ $112.63. The closest option given is A) Faith needs to deposit $112.33 more than Isaac today, acknowledging a slight discrepancy in the final cents due to rounding or calculation differences.

Question 13

Suppose that r and t are greater than zero, which statement is correct?

Accepted Answer

Present value interest factors (PVIF) are calculated as 1 / (1 + r)^t, where r is the interest rate and t is the time period. Since r and t are greater than zero, the denominator is always greater than one, making the PVIF less than one.

Question 14

Compound interest means that you earn:

Accepted Answer

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. This means you earn interest not just on your original investment, but also on the interest that has been added to it over time.

Question 15

You invest $1,000 in an account paying 5% simple interest. You do not add nor withdraw any funds from this account. Every year, your account balance will:

Accepted Answer

With simple interest, the account balance increases by a constant amount each year, which is the interest calculated on the initial principal.

Question 16

Given a constant future value and discount rate, an increase in the number of time periods will _____ the present value.

Accepted Answer

Increasing the number of time periods while keeping the future value and discount rate constant will decrease the present value. This is because the present value is inversely related to the number of time periods when discounting a future amount; the further in the future the amount is received, the less it is worth in present terms.

Question 17

Kurt invests $1,000 at a 10% rate of return for twenty years. The return is based on simple interest that is paid at the end of each year. Which one of the following is correct?

Accepted Answer

Simple interest is calculated only on the principal amount, or on that portion of the principal amount which remains unpaid. Therefore, Kurt will receive the same amount of interest each year.

Question 18

Nadine invests $1,000 at 8% when she is 25 years old. Neal invests $1,000 at 8% when he is 40 years old. Both investments compound interest annually. Both Nadine and Neal retire at age 60. Which one of the following statements is correct?

Accepted Answer

Nadine has more time for her investment to compound, resulting in a larger amount by retirement compared to Neal's shorter investment period.

Question 19

The current value of future cash flows discounted at the appropriate discount rate to current time is called the _____ value.

Accepted Answer

The current value of future cash flows discounted at the appropriate discount rate to current time is called the Present value. This concept is fundamental in finance, reflecting the time value of money.

Question 20

The current value of future cash flows discounted at the appropriate discount rate is called the:

Accepted Answer

The present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows.

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