Question 1

Interest rate: Ray Seo 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?

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Question 2

Compounding: Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest-on-interest after six years?

Accepted Answer

The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money accumulated after n years,
P = the principal (the initial amount of money),
r = the annual interest rate (as a decimal),
n = the number of times the interest is compounded per year, and
t = the number of years.

In this case, P = $17,500, r = 0.0825 (8.25% expressed as a decimal), n = 12 (monthly compounding), and t = 6.

So, A = $17,500(1 + 0.0825/12)^(12*6)
A = $17,500(1.006875)^72
A = $31,997.63

The interest earned is $31,997.63 - $17,500 = $14,497.63.

The interest-on-interest, also known as compound interest on the interest earned, is the difference between the total amount earned and the principal. So, the interest-on-interest is $31,997.63 - $17,500 - $14,497.63, which is equal to $2,497.63.

Therefore, the answer is C, $2,497.63.

Question 3

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.)

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Question 4

Multiple compounding (PV): You need to have $15,000 in five years to payoff 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

We can use the formula for multiple compounding:
PV = FV / (1 + r/n)^(n*t)
where PV is the present value (what we need to find), FV is the future value (which is given as $15,000), r is the interest rate (5.75%), n is the number of compounding periods per year (4 for quarterly), and t is the number of years (5). Substituting the values:
PV = 15000 / (1 + 0.0575/4)^(4*5)
PV = $11,274.89
Rounding to the nearest dollar gives the answer of $11,275, which is choice B.

Question 5

Compounding: Trish Harris has deposited $2,500 today in an account paying 6 percent interest annually. What would be the simple interest earned on this investment in five years? If the account paid compound interest, what would be the interest-on-interest in five years?

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Question 6

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.)

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Question 7

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 CD 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.)

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Question 8

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 percent.

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Question 9

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 CD 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 can use the formula:
Present Value = Future Value / (1 + r)^n
where r is the interest rate and n is the number of years.
In this case, the future value is $25,000, the interest rate is 7.5%, and the number of years is 6.
Therefore, Present Value = $25,000 / (1 + 0.075)^6
                      = $16,199 (rounded to the nearest dollar)
Thus, the best choice is C.

Question 10

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

The present value (PV) can be calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value ($21,000), r is the annual interest rate (0.08), and n is the number of years (3). Plugging in the values: PV = 21000 / (1 + 0.08)^3 = 21000 / 1.2597 ≈ $16,670.

Question 11

Compounding: Richard Delgado invested $10,000 in a money market account that will pay 5.75 percent compounded daily. How much will the interest-on-interest be after two years?

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Question 12

Compounding: Joachim Noah is investing $5,000 in an account paying 6.75 percent annually for three years. What is the interest-on-interest if interest is compounded?

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Question 13

Interest rate: Rachael Steele 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 firm 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 firm, and what is the interest rate if she borrows from her firm? (Round to the nearest percent.)

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Question 14

Present value: Derek's friend, Jackson, 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.)

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Question 15

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 16

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 17

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?

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Question 18

Compounding: Chung Lee wants to invest $3,000 in an account paying 5.25 percent compounded quarterly. What is the interest on interest after four years?

Accepted Answer

The interest on interest is calculated by finding the total compound interest and subtracting the simple interest. The compound interest is $695.98, and the simple interest is $630.00. The difference, which is the interest on interest, is $65.98.

Question 19

Interest rate: Pedro Martinez wants to invest $25,000 in a spa that his sister is starting. He will triple his investment in six years. What is the rate of return that Pedro is being promised? (Rounded to the nearest percent.)

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Question 20

Interest rate: Trayne Rice 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 required interest rate, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value ($5,000 in this case)
P = the principal ($3,000 in this case)
r = the interest rate (what we're trying to find)
n = the number of times interest is compounded per year (since it's not given, we'll assume it's compounded annually)
t = the number of years (3 years in this case)

Plugging in the given values and solving for r, we get:

5,000 = 3,000(1 + r/1)^(1*3)
5/3 = (1 + r)^3
1 + r = (5/3)^(1/3)
r = (5/3)^(1/3) - 1
r ≈ 0.19 or 19% (rounded to the nearest percent)

Therefore, the best choice is A) 19%.

Quiz 5: The Time Value of Money