Question 1

Using lower discount rates will:

Accepted Answer

Lower discount rates will increase the present value of any future cash flow because the lower the discount rate, the less the value of future cash flows is discounted. This means that each future cash flow will have a higher present value when using a lower discount rate.

Question 2

Interest rate: Dominic has $3,000 to invest for three years. He wants to receive $5,000 at the end of the three years. What invest rate would his investment have to earn to achieve his goal? (Round to the nearest percent.)

Accepted Answer

To find the interest rate, we use the formula for compound interest: $ A = P(1 + r)^n $. Here, $ A = 5000 $, $ P = 3000 $, and $ n = 3 $. Solving for $ r $, we get $ 5000 = 3000(1 + r)^3 $. Dividing both sides by 3000 gives $ \frac{5}{3} = (1 + r)^3 $. Taking the cube root of both sides, we find $ 1 + r \approx 1.193 $, so $ r \approx 0.193 $ or 19%.

Question 3

Interest rate: Rachael wants to borrow $6,000 for a period of four years. She has two choices. Her bank is offering to lend her the amount at 7.25 percent compounded annually. She can also borrow from her company and will have to repay a total of $8,130.93 at the end of four years. Should Rachael go with her bank or the company, and what is the interest rate if she borrows from her company? (Round to the nearest percent.)

Accepted Answer

The interest rate for the company loan can be calculated using the formula:A = P(1 + r/n)^(nt)where:A is the total amount to be repaidP is the principal amount borrowedr is the annual interest raten is the number of times per year that the interest is compoundedt is the number of yearsIn this case, we have:A = $8,130.93P = $6,000r = ?n = 1 (compounded annually)t = 4Substituting these values into the formula, we get:$8,130.93 = $6,000(1 + r/1)^(1*4)$8,130.93 = $6,000(1 + r)^4(1 + r)^4 = $8,130.93/$6,000(1 + r)^4 = 1.3551551 + r = 1.1623r = 0.1623 or 16.23%Therefore, the interest rate for the company loan is 16.23%, which is higher than the bank's rate of 7.25%. So, Rachael should go with her bank.

Question 4

Multiple compounding (PV): You need to have $15,000 in five years to pay-off a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.)

Accepted Answer

To find the present value, use the formula PV = FV / (1 + r/n)^(nt). Here, FV = $15,000, r = 0.0575, n = 4, t = 5. Plugging in these values, PV = $15,000 / (1 + 0.0575/4)^(4*5) = $11,275.

Question 5

Multiple compounding (PV): Rick Rodriquez plans to invest some money today so that he will receive $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today?

Accepted Answer

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Question 6

Interest rate: Sofie wants to invest $25,000 in a spa that her sister is starting. She will triple her investment in six years. What is the rate of return that Sofie is being promised? (Rounded to the nearest per cent.)

Accepted Answer

To find the interest rate, we can use the formula:

future value = present value x (1 + interest rate)^n

where n is the number of years and future value is three times the present value (25,000).

So,

75,000 = 25,000 x (1 + interest rate)^6

Dividing both sides by 25,000, we get:

3 = (1 + interest rate)^6

Taking the sixth root of both sides, we get:

1.26 = 1 + interest rate

Subtracting 1 from both sides, we get:

interest rate = 0.26 or 26%

However, this is the nominal annual interest rate. To find the effective annual interest rate, we need to use the formula:

effective annual interest rate = (1 + nominal annual interest rate/n)^n - 1

where n is the number of times interest is compounded in a year. We don't know how often interest is compounded in this case, so let's assume it's compounded monthly (12 times a year).

Then,

effective annual interest rate = (1 + 0.26/12)^12 - 1

= 0.199 or 19.9%

Rounding this to the nearest percent, we get 20%. Therefore, the promised rate of return is 20%.

Question 7

Present value: Tommie Harris is considering an investment that pays 6.5 percent annually. How much must he invest today such that he will have $25,000 in seven years? (Round to the nearest dollar.)

Accepted Answer

To find the present value, use the formula: PV = FV / (1 + r)^n. Here, FV = $25,000, r = 0.065, and n = 7. PV = 25000 / (1.065)^7 = $16,088 (rounded to the nearest dollar).

Question 8

Present value: Derek's friend, Jack, is asking to borrow today with a promise to repay $7,418.87 in four years. If Derek could earn 5.45 percent annually on the any investment he makes today, how much would he be willing to lend Jackson today? (Round to nearest dollar.)

Accepted Answer

The present value of $7,418.87 to be received in four years at 5.45% is $6,000.

Question 9

Multiple compounding (PV): Marcie Witter is saving for her daughter's college education. She wants to have $50,000 available when her daughter graduates from high school in four years. If the investment she is considering will pay 8.25 percent compounded monthly, how much will she have to invest today to reach her target? (Round to the nearest dollar.)

Accepted Answer

To find the present value, use the formula PV = FV / (1 + r/n)^(nt). Here, FV = $50,000, r = 0.0825, n = 12, t = 4. Calculating gives PV ≈ $35,987.

Question 10

Present value: John Hsu wants to start a business in 10 years. He hopes to have $100,000 at that time to invest in the business. To reach his goal, he plans to invest a certain amount today in a bank term deposit that will pay him 9.50 percent annually. How much will he have to invest today to achieve his target? (Round to the nearest dollar.)

Accepted Answer

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Question 11

Interest rate: Ray has $5,000 to invest in a small business venture. His partner has promised to pay him back $8,200 in five years. What is the return earned on this investment?

Accepted Answer

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Question 12

Present value: Becky Sayers wants to buy a house in six years. She hopes to be able to put down $25,000 at that time. If the bank term deposit she wants to invest in will pay 7.5 percent annually, how much will she have to invest today? (Round to the nearest dollar.)

Accepted Answer

To find the present value, we need to use the formula for the present value of a future sum:

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.

In this case, we know that FV = $25,000, r = 7.5%, and n = 6.

Plugging in these values, we get:

PV = $25,000 / (1 + 0.075)6
PV = $16,198.92

Rounding to the nearest dollar, we get a present value of $16,199. Therefore, the best choice is C.

Question 13

Multiple compounding (PV): Joan Alexander wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)

Accepted Answer

To find the present value with monthly compounding, use the formula: PV = FV / (1 + r/n)^(nt). Here, FV = $10,000, r = 0.082, n = 12, t = 3. Calculating gives PV ≈ $7,826.

Question 14

Multiple compounding (PV): Darius Miller is seeking to accumulate $50,000 in six years to invest in a real estate venture. He can earn 6.35 percent annual interest with monthly compounding in a private investment. How much will he have invest today to reach his goal? (Round to the nearest dollar.)

Accepted Answer

Using the formula for multiple compounding (PV), we can find the present value that Darius Miller needs to invest today to reach his goal of $50,000 in six years:

PV = FV / (1 + r/n)^(n*t)

where:
FV = future value = $50,000
r = annual interest rate = 6.35%
n = number of compounding periods per year = 12 (monthly compounding)
t = number of years = 6

Plugging in the values, we get:

PV = 50000 / (1 + 0.0635/12)^(12*6)
PV = $34,193 (rounded to the nearest dollar)

Therefore, the best choice is C: $34,193.

Question 15

Present value: Jack Robbins is saving for a new car. He needs to have $ 21,000 for the car in three years. How much will he have to invest today in an account paying 8 percent annually to achieve his target? (Round to nearest dollar.)

Accepted Answer

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Question 16

The Rule of 72

Accepted Answer

The Rule of 72 is a quick and easy way to estimate how long it will take an investment to double in value at a given interest rate. It is calculated by dividing 72 by the interest rate. For example, if the interest rate is 6%, it will take approximately 12 years to double your investment (72/6=12). Therefore, option A is correct. Option B is incorrect because the Rule of 72 is only accurate for interest rates between 1 and 20 percent. Option C is also incorrect because the formula is actually 72 divided by the interest rate, not 72 divided by i.

Question 17

Interest rate: Your tuition for the coming year is due today. You borrow $8,000 from your uncle and agree to repay in the three years an amount of $9,250. What is the interest rate on this loan? Round to the nearest per cent.

Accepted Answer

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Question 18

Growth rate: Trojan Traps manufactures an innovative mouse trap. Sales this year are $325,000. The company expects its sales to go up to $500,000 in five years. What is the expected growth rate in sales for this company? (Round to the nearest percent.)

Accepted Answer

The expected growth rate can be calculated using the formula for compound annual growth rate (CAGR): CAGR = [(Final Value/Initial Value)^(1/Number of Years)] - 1. Plugging in the values: CAGR = [(500,000/325,000)^(1/5)] - 1 ≈ 0.09 or 9%.

Question 19

Which one of the following statements is NOT true?

Accepted Answer

The future value is not called the discounted value of future cash payments. The future value is the value of the cash payment at a future point in time, while discounted value refers to the present value of that cash payment.

Question 20

Using higher discount rates will:

Accepted Answer

Using higher discount rates will decrease the present value of any future cash flow. This is because a higher discount rate indicates that the investor requires a greater return to compensate for the risks involved in the investment, thus reducing the amount of money they are willing to pay for the future cash flow.

Quiz 5: The Time Value of Money