Question 1

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?

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Question 2

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 $998.25 in your account. If your accountant is correct, what is the current interest rate?

Accepted Answer

We can use the formula for compound interest:

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

where:
A = the amount after t years
P = the principal (starting balance)
r = the annual interest rate (unknown)
n = the number of times the interest is compounded per year (assuming once a year)
t = the number of years

Plugging in the given values, we have:

998.25 = 750(1 + r/1)^(1*3)

Simplifying:

1.331 = 1 + 3r

3r = 0.331

r = 0.1103 or 11.03%

Therefore, the current interest rate is 11 percent (Choice C). However, this is not one of the answer choices given. The closest answer is B, which is 10 percent. This is a reasonable estimate since the actual rate is only slightly higher than 10 percent.

Question 3

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?

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Question 4

Sage decides to cash in all his savings to open a recording studio. He has three accounts to cash in. The first earned 9 percent for two years. The second earned 6 percent for three years. And the last earned 3 percent for six years. Supposing he started with $5,000 in each account, from which account will he get the most cash?

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Question 5

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?

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Question 6

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?

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Question 7

Robert put $15,000 into an account with a fixed interest rate two years ago and now the account balance is $16,695.38. What rate of interest did Robert earn?

Accepted Answer

The interest rate can be calculated using the formula for compound interest: A = P(1 + r)^t. Here, A = $16,695.38, P = $15,000, and t = 2 years. Solving for r gives approximately 5.5%.

Question 8

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 9

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?

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Question 10

George 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 he open his account?

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Question 11

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?

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Question 12

Which of the following is the correct expression for finding the present value of a $1,000 payment one year from today if the interest rate is 6 percent?

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The present value formula is PV = FV/(1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. Using this formula with the given values, we get PV = 1,000/(1 + 0.06)^1 = 943.40. Therefore, the correct expression is C, which gives us the present value.

Question 13

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?

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Question 14

Brittany wants to have about $500,000 when she retires in 10 years. She has $200,000 to deposit now. At which of the following interest rates would her deposit come closest to $500,000 after 10 years?

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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

Account 1 has been collecting interest for the longest period of time, but at a lower interest rate, resulting in a higher balance. Account 2 has a higher interest rate than Account 1, but for a shorter period of time, resulting in a lower balance. Account 3 has the highest interest rate, but for the shortest period of time, resulting in the lowest balance. Therefore, Account 3 has the lowest balance.

Question 16

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?

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Question 17

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 what is the current interest rate?

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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?

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Question 19

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

We can use the compound interest formula to solve this problem:
A = P(1 + r/n)^(nt)
Where:
A = Final amount after 10 years = $983.58
P = Principal amount (initial balance) = $500
r = Annual interest rate (what we want to find)
n = Number of times interest is compounded per year (unknown, but we can assume it's once per year)
t = Time in years = 10

Plugging in the numbers:
$983.58 = $500(1 + r/1)^(1*10)
1.96716 = (1 + r)
r = 0.96716 (converted from decimal to percentage)
r = 9.6716%
Therefore, the current rate of interest is about 7 percent (choice C).

Question 20

Al, Ralph, and Stan are all intending to retire. Each currently has $1 million in assets. Al will earn 16% interest and retire in two years. Ralph will earn 8% interest and retire in four years. Stan will earn 4% interest and retire in eight years. Who will have the largest sum when he retires?

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Quiz 14: The Basic Tools of Finance