Question 1

If you put $250 into an account with a 4 percent interest rate,how many years would you have to wait to have $432.92?

Accepted Answer

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Question 2

At an annual interest rate of 14 percent,about how many years will it take $100 to double in value?

Accepted Answer

Using the rule of 72, we can approximate the number of years it takes for an investment to double by dividing 72 by the annual interest rate.

In this case, 72/14 = 5.14 (rounded to two decimal places). Therefore, it will take approximately 5 years for $100 to double at an annual interest rate of 14 percent.

Therefore, the best choice is C.

Question 3

Which of the following is the correct way to compute the future value of $100 put into an account that earns 4 percent interest for 10 years?

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Question 4

What is the future value of $500 one year from today if the interest rate is 6 percent?

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Question 5

What is the future value of $750 one year from today if the interest rate is 2.5 percent?

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Question 6

At an annual interest rate of 10 percent,about how many years will it take $100 to triple in value?

Accepted Answer

To triple in value, $100 would need to become $300. Using the formula for compound interest, we can determine how long it would take for an initial investment of $100 to grow to $300 at an annual interest rate of 10 percent:

$300 = $100(1 + 0.10)^t

Dividing both sides by $100:

3 = 1.10^t

Taking the logarithm of both sides:

log 3 = log 1.10^t

Using the rule of logarithms that says log a^b = b log a:

log 3 = t log 1.10

Dividing both sides by log 1.10:

t ≈ 11.47

Rounding to the nearest year, it would take about 12 years for $100 to triple in value at an annual interest rate of 10 percent. Therefore, the best choice is C.

Question 7

You put $150 in the bank two years ago and forgot about it.The bank sends you a notice that you now have $169.34 in your account.What interest rate did you earn?

Accepted Answer

We can use the formula for compound interest to solve for the interest rate:
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the interest rate, and n is the number of periods (years in this case).
Plugging in the given values, we get:
169.34 = 150(1 + r)^2
Dividing both sides by 150:
1.129 = (1 + r)^2
Taking the square root of both sides:
1.0625 = 1 + r
Subtracting 1 from both sides:
r = 0.0625 or 6.25%
Therefore, the answer is C.

Question 8

You put $75 in the bank one year ago and forgot about it.The bank sends you a notice that you now have $81 in your account.What interest rate did you earn?

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Question 9

Which of the following is the correct way to compute the future value of $1 put into an account that earns 5 percent interest for 16 years?

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Question 10

Which of the following is the correct way to compute the future value of $X that earns r percent interest for N years?

Accepted Answer

The correct formula for calculating the future value of X with interest rate r for N years is:

X(1 + r)^N

Option B is the only choice that matches this formula, with (1 + r) raised to the power of N. Option A has rN without parentheses, which would lead to incorrect results, and options C and D are not the correct formulas for future value with compound interest. Therefore, the best choice is B.

Question 11

Amelia knows that she has about $105 in her bank account.She knows she earned an interest rate of 4 percent,but she doesn't remember how much she opened the account with a year ago.How much did she put in?

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Question 12

Tim put $275 in the bank one year ago and forgot about it.Today,the bank sent Tim a statement indicating that he now has $294.25 in his account.What interest rate did Tim earn?

Accepted Answer

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

I = P*r*t

Where:
I = Interest earned
P = Principal (initial amount)
r = Interest rate (unknown)
t = Time period (1 year)

We know that the initial amount (P) was $275 and the final amount (P+I) is $294.25, which means that the interest earned (I) is:

I = $294.25 - $275 = $19.25

Substituting these values into the formula, we get:

$19.25 = $275 * r * 1

Solving for r, we get:

r = $19.25 / $275 = 0.07 or 7%

Therefore, Tim earned a 7% interest rate. The answer is C.

Question 13

At an annual interest rate of 10 percent,about how many years will it take $100 to double in value?

Accepted Answer

Using the rule of 72, which is a quick way to estimate the time required for an investment to double in value, we divide 72 by the annual interest rate. So, 72/10 = 7.2 which is closest to option B (7 years). Therefore, B is the best choice.

Question 14

If you presently have $50,000 saved and earn 15 percent interest per year,about how many years will it take for your investment to triple?

Accepted Answer

Using the rule of 72, you can estimate the number of years to triple an investment by dividing 72 by the interest rate. 72 / 15 ≈ 4.8 years to double. To triple, it takes slightly less than two doubling periods, which is approximately 8 years.

Question 15

The future value of a deposit in a savings account will be larger

Accepted Answer

All of the options mentioned in A, B, and C contribute to the increase in the future value of a deposit in a savings account. By waiting longer to withdraw funds, the account has more time to earn interest, which increases the future value. A higher interest rate implies more interest earned over time, which also boosts the future value. Similarly, a larger initial deposit amount means more money to earn interest and leads to a higher future value. Therefore, all three statements are accurate, making choice D the best option.

Question 16

The future value of a deposit in a savings account will be smaller

Accepted Answer

The future value of a deposit in a savings account is directly proportional to the interest rate. So, the lower the interest rate is, the smaller the future value of the deposit will be. The time period and initial deposit size may also affect the future value, but not as significantly as the interest rate. Therefore, option B is the best choice.

Question 17

What is the future value of $450 at an interest rate of 9 percent two years from today?

Accepted Answer

The future value of $450 at an interest rate of 9 percent two years from today is $534.65. This is calculated using the formula FV = PV * (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of years. In this case, PV = $450, r = 9%, and n = 2.

Question 18

What is the future value of $800 one year from today if the interest rate is 7 percent?

Accepted Answer

The future value is calculated using the formula FV = PV * (1 + r), where PV is the present value ($800) and r is the interest rate (0.07). So, FV = $800 * (1 + 0.07) = $856.00.

Question 19

What is the future value of $375 at an interest rate of 3 percent one year from today?

Accepted Answer

Future Value = (Present Value) x (1 + interest rate)
Future Value = $375 x (1 + 0.03)
Future Value = $386.25

Question 20

At an annual interest rate of 20 percent,about how many years will it take $100 to triple in value?

Accepted Answer

Using the formula for compound interest where A is the final amount, P is the principal, r is the annual interest rate, and n is the number of times the interest is compounded per year:
A = P(1 + r/n)^(nt)
We plug in the given values:
300 = 100(1 + 0.2/1)^(1t)
Simplifying and solving for t:
3 = 1.2^t
t ≈ 5.6
Rounding to the nearest whole number, it will take about 6 years for $100 to triple at an annual interest rate of 20 percent. Therefore, the answer is B.

Quiz 14: The Basic Tools of Finance: Present Value Measuring the Time Value of Money