Question 1

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 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

Three people go to the bank to cash in their accounts. Amy had her money in an account for 25 years at 4 percent interest. Bill had his money in an account for 20 years at 5 percent interest. Celia had her money in an account for 5 years at 20 percent interest. If each of them originally deposited $500 in their accounts, which of them gets the most money when they cash in their accounts?

Accepted Answer

The answer of Three people go to the bank to...

Question 4

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 5

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

The answer of Daniel has $300 in a bank account....

Question 6

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 7

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

In the first two years, Jorge earned 5% interest on $1,000, which is $50 per year. So after two years, he would have: 
$1,000 + ($50 x 2) = $1,100

In the third year, he earned 6% interest on $1,100, which is $66.

So the total amount in his account today is: 
$1,100 + $66 = $1,166

The closest answer choice to this amount is B, $1,168.65.

Question 8

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

Using the formula for compound interest, we can solve for the interest rate (r):
A = P(1 + r/n)^(nt)
where A is the final balance, P is the principal (starting balance), r is the interest rate, n is the number of times compounded per year, and t is the number of years.

Plugging in the given values:
A = $983.58
P = $500
n = 1 (compounded annually)
t = 10 years

Solving for r:
A = P(1 + r/n)^(nt)
983.58 = 500(1 + r/1)^(1*10)
983.58/500 = (1 + r)^10
1.96716 = (1 + r)^10
10*log(1.96716) = log(1 + r)
10*0.29366 = log(1 + r)
2.9366 = log(1 + r)
10^2.9366 = 1 + r
841.39 = 1 + r
r = 840.39 = 0.07 (rounded to two decimal places)

Therefore, the current rate of interest is 7 percent.

Question 9

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 10

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 11

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 12

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 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 compound interest: A = P(1+r/n)^(nt), where A is the final amount, P is the principal (starting balance), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. We are given that P = $750, A = $944.78, n = 1 (compounded annually), and t = 3. Plugging these values into the formula, we can solve for r:
$944.78 = $750(1+r/1)^(1*3)
$944.78/$750 = (1+r)^3
1+r = (944.78/750)^(1/3)
1+r = 1.08
r = 0.08 or 8%
Therefore, the current interest rate is 8%, which is 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

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

Although the third account had the highest interest rate, it was only earning that interest for five years, whereas the second account earned interest for twice as long. Therefore, the second account would have a higher balance than the third account now. The first account earned interest for the longest duration, but at a lower rate than the other options, so its balance would be somewhere in between the second and third account. Therefore, the third account with the highest interest rate but shortest duration has the lowest balance now.

Question 16

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...

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

To solve this problem, we need to use the formula for compounding interest:

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

Where:
A = the final amount
P = the principal (the amount initially deposited)
r = the annual interest rate
n = the number of times the interest is compounded per year
t = the time in years

For the first year, we have:
P = $1,000
r = 7% = 0.07
n = 1 (compounded annually)
t = 1

A1 = $1,000(1 + 0.07/1)^(1*1) = $1,070

For the second year, we have:
P = $1,070 (the new principal after the first year)
r = 5% = 0.05
n = 1
t = 1

A2 = $1,070(1 + 0.05/1)^(1*1) = $1,123.50

Therefore, Veronica has $1,123.50 in her account today.

Question 18

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 19

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 20

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:

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

where A is the final amount, P is the principal (initial amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we know that:

- A = $16,917.66
- P = $15,000
- n = 1 (compounded annually)
- t = 2

So we can rearrange the formula to solve for r:

r = (n[(A/P)^(1/nt)] - 1)

Plugging in the values we know:

r = (1[(16,917.66/15,000)^(1/(1*2))] - 1)
r = (1.062 - 1)
r = 0.062 or 6.2%

Therefore, Robert earned a fixed interest rate of 6.2% for two years. So the best choice is C.

Quiz 27: The Basic Tools of Finance

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?

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?

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?

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?

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?

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 $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?

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?

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?

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?

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?

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?

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?

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?

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?

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?