Question 1

The effective rate of interest and compounding frequency have inverse relation.

Accepted Answer

The effective rate of interest increases with more frequent compounding, as interest is calculated and added to the principal more often, leading to higher returns.

Question 2

Your uncle recently sold a rare coin for $28,425; the coin was purchased 10 years ago for $16,800.Your uncle's annual rate of return on his coin investment is 7%.

Accepted Answer

The annual rate of return can be calculated using the formula for compound interest. The actual rate of return is approximately 5.6%, not 7%.

Question 3

A perpetuity is a series of constant or level cash flows that continue for a period not exceeding one-hundred years.

Accepted Answer

A perpetuity is a series of constant or level cash flows that continue indefinitely, not for a period of up to one-hundred years.

Question 4

The loan amortization process involves finding the future payments (over the term of the loan) whose present value at the loan interest rate equals the sum of the amount of initial principal borrowed and the amount of interest on the loan.

Accepted Answer

The answer of The loan amortization process involves finding the...

Question 5

A wealthy art collector has decided to endow her favorite art museum by establishing funds for an endowment which would provide the museum with $1,000,000 per year for acquisitions into perpetuity. The art collector will give the endowment upon her fiftieth birthday 11 years from today. She plans to accumulate the endowment by making annual end-of-year deposits into an account. The rate of interest is expected to be 6 percent in all future periods. How much must the art collector deposit each year to accumulate to the required amount?

Accepted Answer

To accumulate $1,000,000 each year in perpetuity at an interest rate of 6%, we can use the perpetuity formula like this:
PV = PMT / r
where PV is the present value of the perpetuity, PMT is the annual payment, and r is the interest rate.
PV = $1,000,000 / 0.06 = $16,666,667
So the art collector needs to accumulate $16,666,667 in 11 years. We can use the future value formula to find out how much she needs to deposit each year:
FV = PV x (1 + r)^n
where FV is the future value, r is the interest rate, and n is the number of periods.
FV = $16,666,667, PV = 0, r = 0.06, n = 11.
$16,666,667 = PMT x (1 + 0.06)^11
PMT = $16,666,667 / 17.9088
PMT = $930,586.93
So the art collector needs to deposit $930,586.93 at the end of each year for 11 years to accumulate $16,666,667, which will provide the museum with $1,000,000 per year in perpetuity. The closest answer choice is C) $1,264,400, which is not exactly equal to $930,586.93 but is the closest to it.

Question 6

Time value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today.

Accepted Answer

Time value of money is based on the belief that a dollar today is worth more than a dollar that will be received at some future date, due to its potential earning capacity.

Question 7

If a Canada Savings bond can be purchased for $29.50 and has a maturity value at the end of 25 years of $100, what is the annual rate of return on the bond?

Accepted Answer

To calculate the annual rate of return on the bond, we need to use the formula:
Annual rate of return = (Maturity value / Purchase price) ^ (1/years) - 1
Plugging in the numbers, we get:
Annual rate of return = ($100 / $29.50) ^ (1/25) - 1
Annual rate of return = 0.0503 or 5.03%
Therefore, the best choice is B, as it is the closest option to the calculated rate of return.

Question 8

Future Value Interest Factor Annuity (FVIFA) is the future value of $1 ordinary annuity for n period compounded at k percent.

Accepted Answer

This is the definition of FVIFA.

Question 9

You are looking at purchasing a home and would like to obtain $100,000 mortgage amortized over25 years. The current interest rate on a 3-year term is 7% compounded semi-annually. What will your monthly payments be?

Accepted Answer

The answer of You are looking at purchasing a home...

Question 10

Your organization has to borrow some money to build a new factory and has two choices: 1) lenderA charges 6% compounded annually, and 2) lender B charges 5.8% compounded daily. It ischeaper to do business with lender B.

Accepted Answer

Lender B's interest rate may seem lower at first, but when compounded daily, the effective interest rate is actually higher than Lender A's 6% annual rate. Therefore, it is cheaper to do business with Lender A.

Question 11

Given a discount rate of zero percent and n periods of time, the present value interest factor and future value interest factor are equal.

Accepted Answer

When the discount rate is zero percent, the present value interest factor equals 1 for all periods, and the future value interest factor also equals 1 for all periods. Therefore, they are equal.

Question 12

The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is _________.

Accepted Answer

Using the formula for the present value of an ordinary annuity:

PV = C * ((1 - (1 + r)^(-n)) / r)

where PV is the present value, C is the amount of the annuity payment, r is the opportunity cost rate, and n is the number of payments.

Plugging in the values, we get:

PV = $350 * ((1 - (1 + 0.04)^(-5)) / 0.04)
PV = $1,558.03

Therefore, the answer is Choice C, $1,558.

Question 13

You just made your $459 monthly car loan payment and have 22 payments remaining. If your loan rate is at 12% APR, the outstanding balance is $10,241.

Accepted Answer

The outstanding balance calculation involves amortizing the loan, considering the interest rate and remaining payments. The given balance seems incorrect based on typical amortization calculations.

Question 14

For a given interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value.

Accepted Answer

This is because interest is compounded over time, meaning it earns interest on the original amount as well as on any accumulated interest. Therefore, over time the amount of interest earned grows, resulting in a higher future value.

Question 15

Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time.

Accepted Answer

Future value is the value of a current asset at a specified date in the future based on an assumed rate of growth over time. It is calculated by applying compound interest over a specified period of time to the present value.

Question 16

You would like to have a $1,000,000 in 25 years at retirement. Your investments will earn 1% permonth on average. How much do you have to put away at the end of each month to meet yourobjective?

Accepted Answer

To find the monthly investment needed, we use the future value of an annuity formula: FV = Pmt * [(1 + r)^n - 1] / r. Here, FV = $1,000,000, r = 0.01 (1% per month), and n = 300 (25 years * 12 months). Solving for Pmt gives approximately $533.

Question 17

Carol borrows $20,000 from the bank. For a five year loan, the bank requires annual end-of-year payments of $4,878.05. The annual interest rate on the loan is

Accepted Answer

The annual payment of $4,878.05 on a $20,000 loan over five years corresponds to an interest rate of 7 percent. This can be verified using the formula for the annuity payment or by using a financial calculator to solve for the interest rate.

Question 18

Annuity due is an amount that occurs at the beginning of each period.

Accepted Answer

An annuity due is a series of payments or deposits made at the beginning of each period, rather than at the end of each period like a regular annuity.

Question 19

A $10,000 loan at 8% compounded quarterly, with $318.23 per quarter payments, will take 50quarters to pay off.

Accepted Answer

Using the formula for the present value of an annuity, we can calculate that the quarterly payments of $318.23 will pay off the $10,000 loan in exactly 50 quarters. Therefore, the statement is true.

Question 20

The present value of $100 received at the end of year 1, $200 received at the end of year 2, and $300 received at the end of year 3, assuming an opportunity cost of 13 percent, is________ .

Accepted Answer

The present value of $100 received at the end of year 1 is $100 / (1 + 0.13) = $88.49. The present value of $200 received at the end of year 2 is $200 / (1 + 0.13)^2 = $162.82. The present value of $300 received at the end of year 3 is $300 / (1 + 0.13)^3 = $203.69. The present value of all three cash flows is $88.49 + $162.82 + $203.69 = $455.

Quiz 6: Time Value of Money