Question 1

You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 12 percent.

Accepted Answer

The answer of You would like to have enough money...

Question 2

You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5 percent per year, with the first payment of $50,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 10 percent.

Accepted Answer

To calculate the present value of a growing annuity, use the formula: PV = Pmt / (r - g) * [1 - ((1 + g) / (1 + r))^n], where Pmt is the first payment, r is the interest rate, g is the growth rate, and n is the number of periods. Plugging in the values: PV = 50000 / (0.10 - 0.05) * [1 - ((1 + 0.05) / (1 + 0.10))^20] gives approximately $605,604.20.

Question 3

Mr. Williams expects to retire in 30 years and would like to accumulate $1 million in his pension fund. If the annual interest rate is 12 percent, how much should Mr. Williams put into his pension fund each month in order to achieve his goal? (Assume that Mr. Williams will deposit the same amount each month into his pension fund, using monthly compounding.)

Accepted Answer

To find the monthly deposit, we use the future value of an annuity formula: FV = Pmt * [(1 + r)^nt - 1] / r, where FV is the future value ($1,000,000), r is the monthly interest rate (0.12/12), n is the number of years (30), and t is the number of compounding periods per year (12). Solving for Pmt gives approximately $286.13.

Question 4

The present value of a $100 per year perpetuity at 10 percent per year interest rate is $1,000. What would be the present value of this perpetuity if the payments were compounded continuously?

Accepted Answer

The formula for the present value of a perpetuity with continuous compounding is:

PV = C / r

where PV is the present value, C is the annual payment, and r is the interest rate (in decimal form).

Plugging in the values given, we get:

PV = 100 / 0.1 = $1,000

Therefore, the present value remains the same whether it is compounded continuously or not. Thus, the answer is B.

Question 5

A dollar today is worth more than a dollar tomorrow if the interest rate is positive.

Accepted Answer

This is because if the interest rate is positive, then you can earn interest on the dollar today, increasing its value in the future. Therefore, it is preferable to have the dollar today rather than tomorrow.

Question 6

Ms. Colonial has just taken out a $150,000 mortgage at an interest rate of 6 percent per year. If the mortgage calls for equal monthly payments for 20 years, what is the amount of each payment? (Assume monthly compounding or discounting.)

Accepted Answer

The answer of Ms. Colonial has just taken out a...

Question 7

Which of the following statements is true?

Accepted Answer

The process of discounting is essentially the inverse of the process of compounding. Compounding involves taking a present value and calculating its future value based on a specified interest rate and time period. Discounting involves taking a future value and calculating its present value based on the same interest rate and time period. Therefore, the statement in option A is true. Option B is false because compound interest always results in higher ending balances than simple interest at positive interest rates. Option C is false because the present value of an annuity due is always greater than the present value of an equivalent ordinary annuity at positive interest rates. Option D is also false because the future value of an annuity due is always greater than the present value of an equivalent ordinary annuity at positive interest rates.

Question 8

One can find the present value of a future cash flow by dividing it by an appropriate discount factor.

Accepted Answer

The answer of One can find the present value of...

Question 9

You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming a 10 percent annual interest rate, what is the value of this trust?

Accepted Answer

We can use the formula for the present value of a perpetuity:

PV = Payment / Interest rate

Plugging in the given values, we get:

PV = 100,000 / 0.10 = $1,000,000

However, this is the present value four years from now, so we need to discount it back to present value using the formula:

PV = FV / (1 + r)^n

Where FV is the future value, r is the interest rate, and n is the number of years. Plugging in the values, we get:

PV = 1,000,000 / (1 + 0.10)^4 = $683,015.

Question 10

If you invest $100 at 12 percent for three years, how much would you have at the end of three years using compound interest?

Accepted Answer

Using the compound interest formula, we have:
A = P(1 + r/n)^(nt)
where A is the amount at the end of the investment period, P is the principal amount ($100 in this case), r is the interest rate (12% or 0.12), n is the number of times the interest is compounded per year (assuming yearly compounding, n=1), and t is the time period (3 years).
Plugging in the values, we get:
A = 100(1 + 0.12/1)^(1*3)
A = $140.49
Therefore, the best choice is B.

Question 11

The managers of a firm can maximize stockholder wealth by:

Accepted Answer

Projects with positive Net Present Values (NPVs) are expected to generate more cash than the cost of the investment, thus increasing stockholder wealth.

Question 12

You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming a 10 percent annual interest rate, what is the value of this trust?

Accepted Answer

Using the formula for the present value of perpetuity:
PV = C/i, where PV is the present value, C is the cash flow per period (in this case, $100,000 per year), and i is the interest rate.

To find the present value in this case, we need to discount the cash flows back to the present. Since the first payment will not occur for 5 years, we need to discount the cash flows back 5 years.

PV = $100,000 / 0.10 = $1,000,000 (present value of cash flows starting in Year 6)
PV of the trust = PV / (1 + 0.10)^5 = $683,013.

Question 13

An investment at 10 percent compounded continuously has an equivalent annual rate of:

Accepted Answer

The formula for finding the equivalent annual rate for continuous compounding is:
EAR = e^r - 1
Where r is the annual interest rate. 
So, to find the equivalent annual rate for 10% continuous compounding, we plug in 0.1 for r:
EAR = e^0.1 - 1 
EAR = 0.10517 or 10.517%
Therefore, the correct answer is B.

Question 14

You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming an 8 percent annual interest rate, what is the value of this trust?

Accepted Answer

To find the value of the trust, we need to calculate the present value of the perpetual annuity. Since the first payment is in four years, we have to discount the cash flows back to the present day using the given interest rate.

Using the perpetuity formula, the present value of the trust can be calculated as:

Present value = Annual payment amount / Discount rate
Present value = $100,000 / 0.08
Present value = $1,250,000

Now, we need to discount this value back to the present day:

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.

PV = $1,250,000 / (1 + 0.08)^4
PV = $992,290

Therefore, the value of the trust is $992,290. The best choice is B.

Question 15

The concept of compound interest is best described as:

Accepted Answer

Compound interest is the interest earned not only on the principal amount invested, but also on the interest earned over time. In other words, it is interest earned on interest.

Question 16

An investment having a 10.47 percent effective annual rate (EAR)has what APR? (Assume monthly compounding.)

Accepted Answer

The formula to convert EAR to APR with monthly compounding is: APR = (1 + EAR)^(1/12) - 1) * 12. Using this formula, the APR is approximately 10.00 percent.

Question 17

The rate of return, discount rate, hurdle rate, and opportunity cost of capital all have the same meaning.

Accepted Answer

The answer of The rate of return, discount rate, hurdle...

Question 18

You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming an 8 percent annual interest rate, what is the value of this trust?

Accepted Answer

We can use the formula for the present value of a perpetuity:

PV = C / r

where PV is the present value, C is the annual payment, and r is the interest rate.

In this case, C = $100,000 and r = 0.08. However, we need to account for the fact that the first payment will not occur for another 5 years. Therefore, we need to discount the present value by the present value of a 5-year annuity due:

PV = [ C / r ] x [ 1 - (1 + r)^(-n) ] / (1 + r) + C / (1 + r)^n

where n is the number of years until the first payment is made (5).

Plugging in the numbers, we get:

PV = [ $100,000 / 0.08 ] x [ 1 - (1 + 0.08)^(-5) ] / (1 + 0.08) + $100,000 / (1 + 0.08)^5 
PV = $1,235,786.16

Therefore, the value of the trust is $918,787.

Question 19

Mr. Hopper expects to retire in 30 years, and he wishes to accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12 percent per year, how much should Mr. Hopper put into his retirement fund at the end of each year in order to achieve this goal?

Accepted Answer

To solve this, we use the formula for the future value of an annuity, which is FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($1,000,000), P is the annual payment, r is the annual interest rate (12% or 0.12), and n is the number of periods (30 years). Rearranging the formula to solve for P gives us P = FV / [((1 + r)^n - 1) / r]. Plugging in the values gives P = $1,000,000 / [((1 + 0.12)^30 - 1) / 0.12], which calculates to approximately $4,143.66.

Question 20

An investment at 12 percent APR compounded monthly is equal to an effective annual rate of:

Accepted Answer

The formula for effective annual rate is (1 + (APR/n))^n - 1, where n is the number of times compounded in a year. In this case, n = 12 (because it is compounded monthly), so the effective annual rate is (1 + (0.12/12))^12 - 1 = 0.1268, or 12.68%. Therefore, the answer is choice letter A.

Quiz 2: How to Calculate Present Values