Question 1

If a business makes the determination that an investment makes sense at the current interest rate but before they can act the interest rates rises

Accepted Answer

An increase in interest rates would mean a higher cost of borrowing and therefore could affect the return on investment. The business will have to recalculate whether the investment still makes sense at the higher interest rate.

Question 2

If a business makes the determination that an investment makes sense at the current interest rate but before they can act the interest rates fall

Accepted Answer

When interest rates fall, the cost of borrowing decreases, making investments more attractive as the cost of financing them is lower. This generally improves the situation for making the investment.

Question 3

If your broker tells you that a trust to which you are a beneficiary has changed and instead of getting $5000 per year starting next year you will be getting $6000 per year but it will be starting the year after next the present value to you has

Accepted Answer

The present value of the future payments depends on the interest rate used to discount those payments. If the interest rate is relatively high, the delay in payments might reduce their present value despite the increase in the amount. Conversely, if the interest rate is low, the increase in the payment amount might offset the delay's impact, potentially increasing the present value. Therefore, without knowing the interest rate, it's impossible to determine definitively whether the present value has fallen or risen.

Question 4

To determine whether an investment makes sense a business will compute the net present value and if the result is

Accepted Answer

A positive net present value indicates that the investment is expected to generate more value than its total cost, taking into account the time value of money. Therefore, it makes sense for the business to make the investment. A negative net present value would mean that the investment is expected to produce less value than its cost, which would not be a good use of the business's resources. Choice C and D are incorrect because a positive net present value means that the investment is desirable regardless of changes in interest rates.

Question 5

When evaluating a business decision, an economist will often resort to the use of present value because

Accepted Answer

Present value allows for the comparison of the initial investment (which typically occurs in one time period) to the expected profits (which may occur over multiple time periods). This helps the economist determine whether the investment is worth pursuing or not.

Question 6

If your broker tells you that a trust to which you are a beneficiary has changed and instead of getting $5000 per year starting next year you will be getting $6000 per year starting next year the present value to you has

Accepted Answer

The present value to the beneficiary has increased since they will now receive $6000 per year instead of $5000 per year. The increase in the annual payment means that the future cash flows are worth more, therefore the present value has risen.

Question 7

The possibility that an investor will not receive full payment is called

Accepted Answer

The possibility that an investor will not receive full payment is referred to as risk. Risk is a fundamental concept in investing, and investors must carefully consider the risks associated with an investment before making decisions. Options A and B do not adequately describe the scenario presented, and option C is not a commonly used term in finance.

Question 8

The present value of a $1000 payment received 2 years from now at 5% annual interest will be less than $900 because of

Accepted Answer

The present value of a future payment is reduced due to the effect of compounding. At 5% interest, the future value of $1000 in two years would be $1,102.50. Therefore, the present value of $1000 received in two years would be less than $900. Taxes and withholding would not be a factor in determining the present value of a future payment, and double jeopardy is not relevant to finance.

Question 9

If the interest rate is positive, the present value of a stream of payments is

Accepted Answer

The present value of a stream of payments is calculated by discounting each payment back to its present value using the interest rate. If the interest rate is positive, the discounting will decrease the value of each payment, making the sum of the discounted payments less than the sum of the actual payments over time. Therefore, the correct answer is option B.

Question 10

If you are anticipating having to pay $100,000 to a lender 10 years from now and the interest rate rises, the present value of this sum

Accepted Answer

As the interest rate rises, the discount rate used to calculate the present value also increases. Therefore, the present value of the $100,000 future payment will decrease.

Question 11

If you are anticipating having to pay $100,000 to a lender 10 years from now and the interest rate falls, the present value of this sum

Accepted Answer

If the interest rate falls, it becomes cheaper to borrow money, which means that the lender is less likely to demand as much in repayment in order to recoup their investment. Therefore, the present value of the future $100,000 payment would be worth more in today's dollars, causing it to rise.

Question 12

If you have a business opportunity that is pretty much a sure thing that will require you to borrow $1,000,000, but will return to you $200,000 a year in profit for ten years, this is

Accepted Answer

The profitability and wisdom of this investment heavily depend on the interest rate of the borrowed $1,000,000. If the interest rate is such that the annual cost of the loan is less than the $200,000 annual profit, it could be a good investment. Conversely, if the interest costs exceed the annual profit, it would not be wise.

Question 13

If your broker tells you that a trust to which you are a beneficiary has changed and instead of getting $5000 per year starting next year you will be getting $4000 per year starting next year, the present value to you has

Accepted Answer

The present value of the trust's benefits to the beneficiary has fallen because they will now receive $4000 instead of $5000 per year, meaning they will receive less money over time.

Question 14

If the interest rate is positive, the present value of $1000 to be received in ten years is

Accepted Answer

If the interest rate is positive, then the present value of future cash flows is lower than the face value. This is due to the fact that money today is worth more than money in the future, as there is always some level of inflation or the opportunity cost of investing the money elsewhere. Therefore, the present value of $1000 to be received in ten years will be less than $1000 if the interest rate is positive.

Question 15

Using an interest rate of 5%, which figure has the largest present value

Accepted Answer

The present value (PV) of an amount of money is the current value of that amount that would be needed to produce the future value through investment at a given interest rate. The formula for calculating the present value is PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate, and n is the number of periods. Calculating the present value for each option: A) $5000 is already in present value form. B) PV = $5050 / (1 + 0.05)^2 = $4579.59 approximately. C) PV = $5075 / (1 + 0.05)^3 = $4389.39 approximately. D) PV = $5500 / (1 + 0.05)^10 = $3386.38 approximately. Therefore, option A, $5000, has the largest present value.

Question 16

Using an interest rate of 5%, which figure has the smallest present value

Accepted Answer

The present value of a future amount decreases as the time period increases. Therefore, the option that is furthest in the future (option D, $5500 to be received ten years from now) will have the smallest present value. Options A, B, and C are all closer in time and will have larger present values.

Question 17

If payments of $1000 are to be received every year for 20 years and if the interest rate is positive, the present value of this stream will

Accepted Answer

The present value of a stream of payments decreases as the interest rate increases, so it will be less than $1000x20 ($20,000). This is because the higher interest rate means that the money received in the future is worth less in present value terms.

Question 18

If you know that you can afford a $500 per month car payment for the next 48 months, the interest rate is positive and you have found a car dealer who will agree to a zero down payment you will

Accepted Answer

If you can afford a $500 per month car payment for 48 months, your total budget for the car purchase would be $24,000 ($500 x 48 months). Since there is no down payment, the maximum price of the car you can afford would be $24,000 or less. Option A is not possible because a $25,000 car would require a monthly payment higher than $500 for 48 months, and option B is not necessary because you can afford a car less than $24,000. Option D is not relevant to the question because the interest rate is positive, which means it is not zero and can affect the affordability and financing of the car.

Question 19

A 60 month car loan (where no down payment was made)with a 6% interest rate and a monthly payment of $500 would allow the borrower to buy a

Accepted Answer

We can use the formula for present value of an annuity to find the maximum car price that can be financed with the given monthly payment and interest rate over a 60 month period:

PV = Payment * [1 - (1 + r)^(-n)] / r

where PV is the present value (maximum car price), Payment is the monthly payment ($500), r is the interest rate per month (6%/12 = 0.5%), and n is the number of periods (60).

Plugging in the values, we get:

PV = $500 * [1 - (1 + 0.005)^(-60)] / 0.005
PV = $25,862.84

Therefore, the maximum car price that can be financed with a 60 month car loan of $500 per month at 6% interest rate is $25,863. This means that option C) is the best choice.

Question 20

Suppose your grandmother told you (today)that she had set aside an amount of money in a savings account bearing 3% interest that was sufficient to give you a $5,000 graduation present in exactly four years. How much would she have had to set aside?

Accepted Answer

We need to find the present value (PV) of the $5000 gift that will be given in 4 years. We use the formula PV = FV/(1+r)^n, where FV is the future value, r is the interest rate, and n is the number of periods. Plugging in the values, we get PV = $5000/(1.03)^4, which simplifies to $4,289.24 (rounded to the nearest penny). Therefore, our grandmother would have had to set aside $4,289.24 in the savings account. Choice C is the closest to this answer.

Quiz 7: Interest Rates and Present Value