Question 1

The future value of $50,000 deposited today and compounded quarterly at an 8% annual interest rate for seven years is

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r/n)^(nt), where PV = present value, r = annual interest rate, n = number of times the interest is compounded per year, and t = time in years. For this question, PV = $50,000, r = 0.08, n = 4 (since interest is compounded quarterly), and t = 7. Plugging these values into the formula gives FV = $50,000(1 + 0.08/4)^(4*7) = $87,051.

Question 2

Tessa won the lottery for $2,500,000 but due to a change in state laws she will not be able to collect it for three years. Ralph is willing to give her a lump sum today in return for the payment in three years. If current interest rates are 14% per year, how much will Tessa receive today?

Accepted Answer

To find the present value of the future $2,500,000, we use the formula for present value: PV = 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. Plugging in the values: PV = $2,500,000 / (1 + 0.14)^3 ≈ $1,687,430.

Question 3

If $100,000 is invested on December 31, 2016 to earn compound interest semiannually, and if the future value on December 31, 2022, is $225,219 what is the semiannual interest rate on the investment?

Accepted Answer

The correct answer is A because the semiannual interest rate is 7%.

Question 4

The future value of $7,000 deposited today and compounded quarterly at a 16% annual interest rate for five years is

Accepted Answer

The future value is calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount ($7,000), r is the annual interest rate (0.16), n is the number of times interest is compounded per year (4 for quarterly), and t is the number of years (5). Plugging in these values gives FV = 7000(1 + 0.16/4)^(4*5) = $15,338.

Question 5

The future value of $7,000 deposited today and compounded semiannually at an 9% annual interest rate for four years is

Accepted Answer

The future value (FV) of an investment is calculated using the formula FV = PV(1 + r/n)^(nt), where PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. Here, PV = $7,000, r = 9% or 0.09, n = 2 (since the interest is compounded semiannually), and t = 4 years. Plugging these values into the formula gives FV = $7,000(1 + 0.09/2)^(2*4) = $7,000(1.045)^8 ≈ $9,955.

Question 6

What is the formula for the future value of a single amount at compound interest?

Accepted Answer

The formula for the future value (FV) of a single amount at compound interest is $ FV = PV \times (1 + i)^n $, where $PV$ is the present value, $i$ is the interest rate per period, and $n$ is the number of periods. This matches choice B.

Question 7

Table factors for present values

Accepted Answer

Table factors for present values decrease as the number of periods increases because the further in the future a payment is, the less it is worth in today's dollars, assuming a positive interest rate.

Question 8

All of the following are conditions for an ordinary annuity due except

Accepted Answer

An ordinary annuity due involves payments at the beginning of each period, not the end, and its future value is not equal to its present value. The future value is calculated based on the present value, interest rate, and number of periods, and it is typically higher than the present value due to the accumulation of interest.

Question 9

The present value of $500,000 received at the end of five years discounted at 10% is

Accepted Answer

The answer of The present value of $500,000 received at...

Question 10

An annuity is a series of

Accepted Answer

An annuity consists of equal payments made at regular intervals, with interest compounded at the end of each period, which distinguishes it from other types of financial instruments that may involve unequal payments, simple interest, or different compounding intervals.

Question 11

Marco needs $175,000 six years from today. How much should Marco deposit today into an investment account that provides a 12% annual return in order to accomplish his goals?

Accepted Answer

To find out how much Marco should deposit today, we use the formula for the present value of a single future amount: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value (amount to deposit today), FV is the future value ($175,000), r is the annual interest rate (12% or 0.12), and n is the number of years (6). Plugging in the values, we get $PV = \frac{175,000}{(1 + 0.12)^6} \approx $88,660$.

Question 12

Margaret will receive an insurance settlement of $3,000,000 in five years. Randall is willing to give her a lump sum today in return for the payment in five years. If current interest rates are 12% per year, how much will Margaret receive today?

Accepted Answer

To find the present value of the future $3,000,000 that Margaret will receive, we use the present value formula: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years. Plugging in the values: $PV = \frac{3,000,000}{(1 + 0.12)^5} = \frac{3,000,000}{(1.7623)} = $1,702,281$.

Question 13

Bruno deposited $7,500 into an investment account and seven years later, the balance in the account was $10,910. What is the rate of return on this investment if interest is compounded annually?

Accepted Answer

The answer of Bruno deposited $7,500 into an investment account...

Question 14

Each of the following compound interest factors has the same number of periods n) at the same interest rate i). Which one is the table factor for the present value of a single sum?

Accepted Answer

The present value of a single sum factor is always less than 1, as it represents the current value of a sum to be received in the future, discounted at a certain interest rate. Option C, 0.666342, is the only factor less than 1, indicating it is the correct present value factor.

Question 15

On April 1, 2016, Meyers Company purchased a bulldozer. Payment, totaling $70,000, is not due until April 1, 2018. Assuming interest at a 12% annual rate, Meyers should debit Machinery on April 1, 2016, in the amount of

Accepted Answer

The present value of the $70,000 payment due in two years, discounted at a 12% annual rate, is $55,804. This is calculated using the formula for present value: PV = FV / (1 + r)^n, where FV is the future value ($70,000), r is the interest rate (0.12), and n is the number of years (2).

Question 16

Mildred desires to have $7,049 on deposit five years from today. If she has $4,000 to deposit, what rate of interest, compounded annually, must be obtained to accumulate the desired $7,049 in five years?

Accepted Answer

The answer of Mildred desires to have $7,049 on deposit...

Question 17

All of the following are conditions for an ordinary annuity except

Accepted Answer

For an ordinary annuity, interest is not compounded in the middle of each time period; instead, payments are made at the end of each period.

Question 18

What is the formula for the present value of a single sum at compound interest?

Accepted Answer

The formula for the present value (PV) of a single future sum (FV) at compound interest is $ F V \times \frac{1}{(1+i)^{n}} $, where $i$ is the interest rate per period, and $n$ is the number of periods. This formula is used to determine the current value of a future amount of money given a specified rate of return.

Question 19

Maxine has $1,000 to invest today. How much will her money be worth in 15 years if she earns 9% compounded semiannually on her money?

Accepted Answer

The future value of an investment is calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount ($1,000), r is the annual interest rate (9% or 0.09), n is the number of times the interest is compounded per year (2 for semiannually), and t is the time the money is invested for (15 years). Plugging in the values, we get FV = $1,000(1 + 0.09/2)^(2*15) = $3,745.

Question 20

All of the following are conditions for an annuity due except

Accepted Answer

In an annuity due, payments are made at the beginning of each period, not at the end, which contradicts the compounding of interest at the end of each period as stated in option D.

Quiz 23: Understanding Time Value of Money Formulas and Concepts