Question 1

The amount you must deposit now in your savings account, paying 6% interest, in order to accumulate $6,000 for a down payment 5 years from now on a new car is

Accepted Answer

To find the present value (the amount you must deposit now) to accumulate a future sum, you use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value ($6000), r is the interest rate per period (6% or 0.06), and n is the number of periods (5 years). Plugging in the values: PV = $6000 / (1 + 0.06)^5 ≈ $4484.

Question 2

The present value of $10,000 to be received in 5 years will be smaller if the discount rate is

Accepted Answer

The present value of a future cash flow decreases as the discount rate increases. If the discount rate is increased, the present value of the $10,000 to be received in 5 years will be smaller.

Question 3

If $40,000 is put in a savings account paying interest of 4% compounded annually, what amount will be in the account at the end of 5 years?

Accepted Answer

The answer of If $40,000 is put in a savings...

Question 4

If $30,000 is deposited in a savings account at the end of each year and the account pays interest of 5% compounded annually, what will be the balance of the account at the end of 10 years?

Accepted Answer

To solve this problem, we can use the formula for compound interest:

$A=P(1+r)^n$

where A is the ending balance, P is the principal (or starting balance), r is the interest rate, and n is the number of compounding periods.

In this case, the principal (P) is $0 (because there is no starting balance), the interest rate (r) is 5%, and the compounding period (n) is 10 (since the question asks about 10 years).

Now we just need to find the ending balance (A) by plugging in the numbers:

$A = 30,000(1+0.05)^{10}$

Using a calculator, we get:

$A \approx 377,337$

So the balance of the account at the end of 10 years is approximately $377,337.

Therefore, the answer is C.

Question 5

Which of the following is not necessary to know in computing the future value of an annuity?

Accepted Answer

While the year in which the payments begin can impact the timing of the future value calculation, it is not necessary information for computing the future value of an annuity. The amount of the periodic payments, interest rate, and number of compounding periods are all essential components in determining the future value.

Question 6

All of the following are necessary to compute the future value of a single amount except the

Accepted Answer

The future value of a single amount is calculated based on the principal (present value), interest rate, and number of periods. The maturity value is the future value already calculated and is not necessary to compute it.

Question 7

Which of the following accounting problems does not involve a present value calculation?

Accepted Answer

The declining-balance depreciation expense is calculated based on a predetermined rate applied to the asset's book value, and does not involve present value calculations. The other options all involve present value calculations in order to determine the appropriate amount to report on the financial statements.

Question 8

If the single amount of $3,000 is to be received in 3 years and discounted at 6%, its present value is

Accepted Answer

Using the formula for present value of a single amount: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. Plugging in the given values, we get PV = 3,000 / (1 + 0.06)^3 = $2,519.

Question 9

If you are able to earn an 8% rate of return, what amount would you need to invest to have $30,000 one year from now?

Accepted Answer

To solve the problem, we can use the formula:
Future Value = Present Value x (1 + Rate of Return)
Plugging in the given values, we get:
30,000 = Present Value x (1 + 0.08)
Simplifying the right side, we get:
30,000 = Present Value x 1.08
Dividing both sides by 1.08, we get:
Present Value = 27,777.78 (rounded to nearest cent)
Therefore, the best choice is B, $27,778.

Question 10

If the single amount of $2,000 is to be received in 2 years and discounted at 11%, its present value is

Accepted Answer

Using the formula for present value of a single amount: PV = FV ÷ (1 + r)n, where PV is present value, FV is future value, r is the discount rate, and n is the number of periods.

PV = 2,000 ÷ (1 + 0.11)2
PV = 2,000 ÷ (1.11)2
PV = 2,000 ÷ 1.2321
PV = 1,622.83
Rounding to the nearest dollar, we get $1,623 as the present value.

Question 11

Which table has a factor of 1.00000 for 1 period at every interest rate?

Accepted Answer

The answer of Which table has a factor of 1.00000...

Question 12

The future value of an annuity factor for 2 periods is equal to

Accepted Answer

The answer of The future value of an annuity factor...

Question 13

Present value is based on

Accepted Answer

All three factors - dollar amount, time, and interest rate - are considered in determining the present value of a future amount. Therefore, all answer choices are correct.

Question 14

If you are able to earn a 15% rate of return, what amount would you need to invest to have $15,000 one year from now?

Accepted Answer

We can use the formula: FV = PV x (1 + r), where FV is the future value, PV is the present value, and r is the rate of return as a decimal. Rearranging the formula, we get PV = FV / (1 + r). Plugging in the given values, we get PV = 15000 / (1 + 0.15) = 13043.48, which is closest to option D.

Question 15

In present value calculations, the process of determining the present value is called

Accepted Answer

The process of determining the present value involves discounting future cash flows by a certain rate, which is why it is referred to as discounting. Allocating is the process of distributing resources or funds, pricing is setting a value or cost for a product or service, and negotiating is the process of discussing and reaching an agreement between parties. These terms do not accurately describe the process of determining present value.

Question 16

The future value of 1 factor will always be

Accepted Answer

The future value of 1 factor represents the amount that $1 will grow to at a given interest rate over a certain number of periods. As long as the interest rate is positive, the future value will always be greater than 1, meaning that the initial $1 investment grows over time.

Question 17

The amount you must deposit now in your savings account, paying 5% interest, in order to accumulate $10,000 for your first tuition payment when you start college in 3 years is

Accepted Answer

We can use the formula for compound interest:

$A=P(1+r)^n$

where:

A = final amount (in this case, $10,000)
P = initial principal (what we are trying to find)
r = interest rate as a decimal (5% = 0.05)
n = number of compounding periods (3 years = 3)

Substituting in the values we know:

$10,000 = P(1+0.05)^3$

$10,000 = P(1.157625)$

$P = \frac{10,000}{1.157625}$

$P \approx 8,638$

Therefore, we must deposit approximately $8,638 now in order to accumulate $10,000 in 3 years with 5% interest. Choice C is the closest to this value.

Question 18

McGoff Company deposits $20,000 in a fund at the end of each year for 5 years.The fund pays interest of 4% compounded annually.The balance in the fund at the end of 5 years is computed by multiplying

Accepted Answer

The balance in the fund at the end of 5 years is the future value of an annuity, which represents the accumulated value of a series of equal payments made at regular intervals, in this case $20,000 at the end of each year for 5 years, with interest compounded annually at 4%. Therefore, the correct choice is D.

Question 19

Which of the following discount rates will produce the smallest present value?

Accepted Answer

The higher the discount rate, the smaller the present value. Therefore, out of the given options, 10% would produce the smallest present value.

Question 20

Suppose you have a winning lottery ticket and you are given the option of accepting $3,000,000 three years from now or taking the present value of the $3,000,000 now.The sponsor of the prize uses a 6% discount rate.If you elect to receive the present value of the prize now, the amount you will receive is

Accepted Answer

To calculate the present value of the $3,000,000 to be received three years from now, we need to use the formula:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the discount rate, and n is the number of years.
Plugging in the values given, we get:
PV = 3,000,000 / (1 + 0.06)^3
PV = 3,000,000 / 1.191016
PV = $2,518,860
Therefore, the best choice would be to take the present value of $2,518,860 now as it is lower than the $3,000,000 to be received in the future, but still a substantial amount.

Quiz 14: Understanding Investments in Debt and Equity Securities