Question 1

On the Internet you find the following offers for opening an online account. Which of them is the best offer if you have $2,000 to save for two years?

Accepted Answer

The answer of On the Internet you find the following...

Question 2

The future value of $500 saved for two years at an interest rate of 5% is

Accepted Answer

To calculate future value, we use the formula FV = PV*(1+r)^n, where PV is the present value, r is the interest rate, and n is the number of periods. Plugging in the values, we get FV = 500*(1+0.05)^2 = $551.25, which is closest to choice C.

Question 3

If you put $1,000 in the bank today at an interest rate of 6% what is its value in two years?

Accepted Answer

The value of the investment in two years can be calculated by using the formula A=P(1+r)n where A is the value after n years, P is the principal (initial investment), r is the interest rate, and n is the number of years. Plugging in the given values, A = 1000(1+0.06)2 = $1,123.60. Therefore, the correct choice is C.

Question 4

If you deposit $900 into an account for two years and the interest rate is 4%, how much do you have at the end of the two years?

Accepted Answer

The formula for calculating compound interest is: 
A = P(1 + r/n)^(nt) 
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)

In this case, P = $900, r = 0.04 (4%), n = 1 (compounded annually), and t = 2 (two years).

Plugging in the values, we get:
A = 900(1 + 0.04/1)^(1*2)
A = $973.44

Therefore, the best choice is B, which is $973.44.

Question 5

In answering which of the following questions would you find it necessary to calculate a future value?

Accepted Answer

In order to determine how much Jill will have in her bank account after 2 years, it is necessary to calculate the future value of her initial investment of $5,000 at a 3 percent interest rate over 2 years. The other questions do not require a future value calculation.

Question 6

Will is risk averse and has $1,000 with which to make a financial investment. He has three options. Option A is a risk-free government bond that pays 5 percent interest each year for two years. Option B is a low-risk stock that analysts expect to be worth about $1,102.50 in two years. Option C is a high-risk stock that is expected to be worth about $1,200 in four years. Will should choose

Accepted Answer

Will is risk averse and is likely to prefer the risk-free government bond over the other two options. This option provides a guaranteed return and the interest rate of 5 percent is relatively high compared to current market rates, making it the best choice for Will's risk tolerance. Option B involves some risk and the potential return of $102.50 is not significant enough to outweigh the risk for Will. Option C is too risky for Will's risk tolerance and the longer time horizon makes it less desirable.

Question 7

On the Internet you find the following offers for opening an online account. Which of them is the best offer if you have $5,000 to save for two years?

Accepted Answer

The answer of On the Internet you find the following...

Question 8

What is the present value of a payment of $2,000 to be received two years from today if the interest rate is 5%?

Accepted Answer

The answer of What is the present value of a...

Question 9

According to the rule of 70, if a person's saving doubles in 10 years, what interest rate were they earning?

Accepted Answer

The answer of According to the rule of 70, if...

Question 10

You receive $500 today which you plan to save for two years. Also, in two years you will be given another $500. If the interest rate is 5 percent, what is the present value of the payment of $500 today and the $500 in two years?

Accepted Answer

The present value of $500 today is $500, and the present value of $500 received in two years is $500 divided by (1.05)^2.

Question 11

Using the rule of 70, about how much would $100 be worth after 50 years if the interest rate were 7 percent?

Accepted Answer

The answer of Using the rule of 70, about how...

Question 12

Which of the following has the highest future value?

Accepted Answer

The answer of Which of the following has the highest...

Question 13

Albert Einstein once referred to compounding as

Accepted Answer

Albert Einstein referred to compounding as "the greatest mathematical discovery of all time."

Question 14

Which famous person referred to compounding as "the greatest mathematical discovery of all time?"

Accepted Answer

Albert Einstein referred to compounding as "the greatest mathematical discovery of all time."

Question 15

In answering which of the following questions would you find it necessary to calculate a present value?

Accepted Answer

The answer of In answering which of the following questions...

Question 16

You are tearing down a building and find $1 in change that someone lost when working on the building 140 years ago. If, instead of being careless with the $1 in change, this person had deposited it into a bank and earned 2 percent interest every year for 140 years, how much would be in the account today according to the rule of 70?

Accepted Answer

The rule of 70 states that to find the approximate number of years it takes for a certain value to double at a given interest rate, you divide 70 by the interest rate. In this case, 70 divided by 2 is 35, which means the value of the $1 would double every 35 years. After 140 years, it would have doubled four times, making it worth $16 ($1 doubled four times is $16). Therefore, the answer is choice C.

Question 17

Fourteen years ago William put money in his account at First National Bank. William decides to cash in his account and is told that his money has quadrupled. According to the rule of 70, what rate of interest did Alfred earn?

Accepted Answer

The rule of 70 states that to find the approximate number of years for an investment to double in value, divide 70 by the interest rate (assuming the interest is compounded annually).

In this case, William's money quadrupled, so it doubled twice. Therefore, we need to divide 70 by 2 to find out what interest rate would cause an investment to double twice in 14 years.

70/2 = 35

So the interest rate is approximately 35.

To check our answer, we can use the formula for compound interest:

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

Where A is the end amount, P is the principal (initial amount), r is the interest rate, n is the number of times per year the interest is compounded, and t is the number of years.

If William's money quadrupled, then his end amount (A) is four times his initial amount (P). Let's say he initially deposited $100.

4P = 400

P = 100

So his initial amount was $100.

We know he has earned compound interest for 14 years, so t = 14. Let's assume that the interest is compounded annually (n = 1).

4P = P(1 + r/1)^(1*14)

4 = (1 + r)^14

Taking the 14th root of both sides:

1 + r = 4^(1/14)

1 + r = 1.1001

(r = 0.1001 or 10.01%)

So the interest rate that would cause William's money to quadruple in 14 years is approximately 10%.

Therefore, the best choice is C) 10 percent.

Question 18

Twenty years ago, Dr. Montgomery borrowed money from her parents to pay her tuition at graduate school. Now she wants to pay them back. She gives them double what they gave her. According to the rule of 70, what interest rate would have given her parents the same amount of money if they had put it in the bank rather than lending it to their daughter?

Accepted Answer

The answer of Twenty years ago, Dr. Montgomery borrowed money...

Question 19

What is the present value of a payment of $1,000 two years from now if the interest rate is 6%?

Accepted Answer

To calculate the present value of a future payment, we need to discount it by the interest rate. Using the formula PV = FV / (1 + r)n, where PV is present value, FV is future value, r is the interest rate, and n is the number of years, we get:
PV = $1000 / (1 + 0.06)2
PV = $1000 / 1.1236
PV ≈ $890.99
Therefore, the best choice is B, which represents $1000 divided by (1.06)2, the correct calculation for the present value.

Question 20

Nancy would like to double the money in her retirement account in five years. According to the rule of 70, what rate of interest would she need to earn to attain her objective?

Accepted Answer

The answer of Nancy would like to double the money...

Quiz 9: The Basic Tools of Finance