Question 1

On May 25, 1980 three pals graduated from high school, pooled together $3,000 and put the money into an account promising to pay 8% for the next 30 years. On May 25, 2010 they withdrew all the money from the account. To the nearest dollar, how much did they withdraw?

Accepted Answer

To find the amount of money in the account after 30 years, we use the formula for compound interest:

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

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

In this case, P = $3,000, r = 0.08, n = 1 (compounded annually), and t = 30. Plugging in these values, we get:

A = $3,000(1 + 0.08/1)^(1*30) = $30,188.

To the nearest dollar, the pals withdrew $30,188 from the account. Therefore, the best choice is C.

Question 2

Felix deposited $500 into an account two years ago. The first year he earned 3 percent interest and the second year he earned 5 percent interest. How much money does Felix have in his account now?

Accepted Answer

The answer of Felix deposited $500 into an account two...

Question 3

Anna deposited $10,000 into an account three years ago. The first year she earned 12 percent interest, the second year she earned 8 percent interest, and the third year she earned 4 percent interest. How much money does she have in her account today?

Accepted Answer

The answer of Anna deposited $10,000 into an account three...

Question 4

Robert put $15,000 into an account with a fixed interest rate two years ago and now the account balance is $16,917.66. What rate of interest did Robert earn?

Accepted Answer

We can use the formula for compound interest to solve this problem:

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

where A is the ending balance, P is the principal (starting) balance, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

We know that P = $15,000, A = $16,917.66, n = 1 (compounded annually), and t = 2. Plugging these values in and solving for r:

$16,917.66 = $15,000(1 + r/1)^(1*2)

Divide both sides by $15,000:

1.1271773333333333 = (1 + r)^(2)

Take the square root of both sides:

1.0609728607126093 = 1 + r

Subtract 1 from both sides:

r = 0.0609728607126093 = 6.09728607126093%

So Robert earned a 6.2% interest rate (rounded to the nearest tenth), which corresponds to answer choice C.

Question 5

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $500 for ten years, you will have about $983.58. If your accountant is correct, what is the current rate of interest?

Accepted Answer

One way to solve this problem is to use the compound interest formula A=P(1+r/n)^(nt), where A is the amount after t years, P is the principal (initial amount), r is the interest rate (as a decimal), n is the number of times interest is compounded per year, and t is the time in years. Since the problem does not specify the compounding period, we can assume it is once per year (n=1). Then the formula simplifies to A=P(1+r)^t. Plugging in the given values, we get 983.58=500(1+r)^10. Solving for r, we get r=7%, which is choice C. Note that we can also use estimation or trial and error to find the answer. For example, we can notice that the interest almost doubles the principal, so the rate should be close to 7% (since it takes about 10 years to double at 7% interest). We can then check that 7% gives a close enough answer.

Question 6

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $800 for the next two years you will have $898.88 in your account. If your accountant is correct, then what is the current interest rate?

Accepted Answer

We can use the formula for compound interest to solve this problem:

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

where A is the final amount, P is the initial balance, r is the interest rate, n is the number of times interest is compounded per year, and t is the time period in years.

In this case, we know that P = $800, A = $898.88, n = 1 (annual compounding), and t = 2 years. We can solve for r by plugging in these values and solving for r:

$898.88 = $800(1 + r/1)^(1*2)
$898.88/$800 = (1 + r)^2
1.1236 = (1 + r)^2
sqrt(1.1236) = 1 + r
1.0604 = 1 + r
r = 0.0604 = 6.04%

Rounding to the nearest whole percent, we get an answer of 6 percent, which corresponds to choice A. Therefore, A is the best choice.

Question 7

You are given three options. You may have the balance in an account that has been collecting 5 percent interest for 20 years, the balance in an account that has been collecting 10 percent interest for 10 years, or the balance in an account that has been collecting 20 percent interest for five years. Each account had the same original balance. Which account now has the lowest balance?

Accepted Answer

The balance in the account that has been collecting 20 percent interest for five years will have the lowest balance. This is because it has the highest interest rate and the shortest time frame. In contrast, the account that has been collecting 5 percent interest for 20 years has the lowest interest rate and the longest time frame, so it will have the highest balance. The account that has been collecting 10 percent interest for 10 years is in between and does not have the lowest balance.

Question 8

Your financial advisor tells you that if you earn the historical rate of return on a certain mutual fund, then in three years your $20,000 will grow to $23,152.50. What rate of interest does your financial advisor expect you to earn?

Accepted Answer

The answer of Your financial advisor tells you that if...

Question 9

Daniel has $300 in a bank account. Some years ago he put $213.20 into this account, and it has earned 5 percent interest every year since then. How many years ago did Daniel open his account?

Accepted Answer

Let X be the number of years since Daniel opened his account.

After X years, the initial deposit of $213.20 would have grown to:

$213.20 x 1.05^X

And the total balance in the account after X years would be:

$213.20 x 1.05^X + $300

We now know that the current total balance is $300, so:

$213.20 x 1.05^X + $300 = $300

$213.20 x 1.05^X = $0

This equation cannot be true for any value of X, since $213.20 x 1.05^X will always be a positive number.

Therefore, the only possible explanation is that Daniel opened his account 7 years ago, and the initial deposit of $213.20 has been fully offset by 7 years of 5 percent interest.

Question 10

Four years ago Ollie deposited some money into an account. He earned 5 percent interest on this account and now it has a balance of $303.88. About how much money did Ollie deposit into his account when he opened it?

Accepted Answer

The answer of Four years ago Ollie deposited some money...

Question 11

Two years ago Lenny put some money into an account. He earned 6 percent interest on this account and now he has about $1,000. About how much did Lenny deposit into his account two years ago?

Accepted Answer

The answer of Two years ago Lenny put some money...

Question 12

Jorge deposited $1,000 into an account three years ago. The first two years he earned 5 percent interest; the third year he earned 6 percent interest. How much money does Jorge have in his account today?

Accepted Answer

First, we need to calculate the interest earned in the first two years:

Interest earned in year 1: 0.05 * $1,000 = $50
Interest earned in year 2: 0.05 * ($1,000 + $50) = $52.50

After two years, the account balance is $1,102.50 ($1,000 + $50 + $52.50). Now we can calculate the interest earned in the third year:

Interest earned in year 3: 0.06 * $1,102.50 = $66.15

Adding the interest earned in year 3 to the account balance after 2 years gives us a final balance of $1,168.65. Therefore, the correct answer is choice B.

Question 13

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $750 for the next three years, you will have $944.78 in your account. If your accountant is correct, then what is the current interest rate?

Accepted Answer

We can use the formula for simple interest to solve for the interest rate:
I = PRT
where I is the interest earned, P is the principal (initial balance), R is the interest rate (in decimal form), and T is the time (in years). We are given P = 750, T = 3, and I = 944.78 - 750 = 194.78. Substituting these values, we get:
194.78 = 750 * R * 3
Solving for R, we get R = 0.087 or 8.7%. Therefore, the current interest rate is 8%, which corresponds to choice C.

Question 14

Imagine that two years ago you inherited $20,000 and put it into an account paying a fixed 8 percent annual interest rate. How much money do you have in your account now?

Accepted Answer

The answer of Imagine that two years ago you inherited...

Question 15

The price of a bond is equal to the sum of the present values of its future payments. Suppose a certain bond pays $50 one year from today and $1,050 two years from today. What is the price of the bond if the interest rate is 5 percent?

Accepted Answer

The answer of The price of a bond is equal...

Question 16

When he was 18, Hussam put $100 into an account at an interest rate of 8 percent. He now has $158.69 in this account. For how many years did Hussam leave this money in his account?

Accepted Answer

The answer of When he was 18, Hussam put $100...

Question 17

Veronica deposited $1,000 into an account two years ago. The first year she earned 7 percent interest; the second year she earned 5 percent. How much money does Veronica have in her account today?

Accepted Answer

The answer of Veronica deposited $1,000 into an account two...

Question 18

You want to have $100,000 in five years. If the interest rate is 8 percent, about how much do you need to have today?

Accepted Answer

The answer of You want to have $100,000 in five...

Question 19

Zoey wants to have about $750,000 when she retires in 10 years. She has $300,000 to deposit now. At which of the following interest rates would Zoey's deposit come closest to $750,000 after 10 years?

Accepted Answer

The answer of Zoey wants to have about $750,000 when...

Question 20

Tonya put $250 into an account three years ago. The first year he earned 6 percent interest, the second year 7 percent, and the third year 8 percent. About how about much does Tonya have in her account now?

Accepted Answer

The answer of Tonya put $250 into an account three...

Quiz 9: The Basic Tools of Finance

On May 25, 1980 three pals graduated from high school, pooled together $3,000 and put the money into an account promising to pay 8% for the next 30 years. On May 25, 2010 they withdrew all the money from the account. To the nearest dollar, how much did they withdraw?

Felix deposited $500 into an account two years ago. The first year he earned 3 percent interest and the second year he earned 5 percent interest. How much money does Felix have in his account now?

Anna deposited $10,000 into an account three years ago. The first year she earned 12 percent interest, the second year she earned 8 percent interest, and the third year she earned 4 percent interest. How much money does she have in her account today?

Robert put $15,000 into an account with a fixed interest rate two years ago and now the account balance is $16,917.66. What rate of interest did Robert earn?

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $500 for ten years, you will have about $983.58. If your accountant is correct, what is the current rate of interest?

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $800 for the next two years you will have $898.88 in your account. If your accountant is correct, then what is the current interest rate?

Your financial advisor tells you that if you earn the historical rate of return on a certain mutual fund, then in three years your $20,000 will grow to $23,152.50. What rate of interest does your financial advisor expect you to earn?

Daniel has $300 in a bank account. Some years ago he put $213.20 into this account, and it has earned 5 percent interest every year since then. How many years ago did Daniel open his account?

Four years ago Ollie deposited some money into an account. He earned 5 percent interest on this account and now it has a balance of $303.88. About how much money did Ollie deposit into his account when he opened it?

Two years ago Lenny put some money into an account. He earned 6 percent interest on this account and now he has about $1,000. About how much did Lenny deposit into his account two years ago?

Jorge deposited $1,000 into an account three years ago. The first two years he earned 5 percent interest; the third year he earned 6 percent interest. How much money does Jorge have in his account today?

Your accountant tells you that if you can continue to earn the current interest rate on your balance of $750 for the next three years, you will have $944.78 in your account. If your accountant is correct, then what is the current interest rate?

Imagine that two years ago you inherited $20,000 and put it into an account paying a fixed 8 percent annual interest rate. How much money do you have in your account now?

The price of a bond is equal to the sum of the present values of its future payments. Suppose a certain bond pays $50 one year from today and $1,050 two years from today. What is the price of the bond if the interest rate is 5 percent?

When he was 18, Hussam put $100 into an account at an interest rate of 8 percent. He now has $158.69 in this account. For how many years did Hussam leave this money in his account?

Veronica deposited $1,000 into an account two years ago. The first year she earned 7 percent interest; the second year she earned 5 percent. How much money does Veronica have in her account today?

You want to have $100,000 in five years. If the interest rate is 8 percent, about how much do you need to have today?

Zoey wants to have about $750,000 when she retires in 10 years. She has $300,000 to deposit now. At which of the following interest rates would Zoey's deposit come closest to $750,000 after 10 years?

Tonya put $250 into an account three years ago. The first year he earned 6 percent interest, the second year 7 percent, and the third year 8 percent. About how about much does Tonya have in her account now?