Question 1

Suppose a family wants to save $60,000 for a child's tuition. The child will be attending college in 18 years. For simplicity, assume the family is saving for a one-time college tuition payment. If the interest rate is 6%, then about how much does this family need to deposit in the bank today?

Accepted Answer

To find out how much the family needs to deposit today, we use the formula for the present value of a future sum of money, which is $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value, FV is the future value ($60,000), r is the annual interest rate (6% or 0.06), and n is the number of years (18). Plugging in the values, we get $PV = \frac{60,000}{(1 + 0.06)^{18}}$, which calculates to approximately $21,000.

Question 2

Compound interest means that:

Accepted Answer

Compound interest means that the interest earned on an investment or loan is added to the principal amount and interest is then earned on the new total. This results in interest on interest, which is the essence of compound interest.

Question 3

Which of the following best expresses the proceeds a lender receives from a one-year simple loan when the annual interest rate equals i?

Accepted Answer

The formula for calculating the proceeds a lender receives from a one-year simple loan is principal amount (PV) multiplied by one plus the annual interest rate (i), or PV(1 + i). This represents the total amount to be repaid at the end of the year, including both the principal and the interest. Option A only adds the interest to the principal, while option B divides the future value (FV) by the interest rate, which is not a relevant calculation for this question. Option D divides the principal by the interest rate, which also does not provide an accurate answer.

Question 4

A promise of a $100 payment to be received one year from today is:

Accepted Answer

If the interest rate is zero, there is no benefit or cost to receiving the payment today or one year from today, as the value of money remains the same. Therefore, a promise of a $100 payment to be received one year from today would be equally valuable as receiving the payment today.

Question 5

Suppose Mary receives an $8,000 loan from First National Bank. Mary repays $8,480 to First National Bank at the end of one year. Assuming the simple calculation of interest, the interest rate on Mary's loan was:

Accepted Answer

The interest on Mary's loan can be calculated using the formula:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate and Time is the time period for which the loan was taken.

In this case, the Principal is $8,000, Time is 1 year, and the amount repaid (including interest) is $8,480.

Therefore, Interest = $8,480 - $8,000 = $480

Using the formula for interest, we can find the interest rate as:

Rate = (Interest / Principal) x 100 x (1 / Time)

Substituting the values we get,

Rate = (480 / 8000) x 100 x (1/1) = 6.00%

Hence, the interest rate on Mary's loan was 6.00%.

Question 6

Which of the following expresses 4.85%?

Accepted Answer

To express a percentage as a decimal, divide by 100. Thus, 4.85% as a decimal is 4.85/100 = 0.0485.

Question 7

Suppose that Stephen Curry, a basketball player for the Golden State Warriors, will become a free agent at the end of this NBA season. Suppose that Curry is considering two possible contracts from different teams. Note that the salaries are paid at the end of EACH year. 
The interest rate is 10%. Based on this information, which of the following is true?

Accepted Answer

To determine the present value of each contract, we need to calculate the present value of each year's salary and add them up.

For the Boston contract:
- Year 1 salary: $10 million
- Year 2 salary: $11 million
- Year 3 salary: $12 million
PV = 10/(1+0.1)^1 + 11/(1+0.1)^2 + 12/(1+0.1)^3 = $28,065,020

For the Portland contract:
- Year 1 salary: $12 million
- Year 2 salary: $12 million
- Year 3 salary: $12 million
PV = 12/(1+0.1)^1 + 12/(1+0.1)^2 + 12/(1+0.1)^3 = $30,925,043

Therefore, Curry should take the Portland contract because it has a higher present value of $30,925,043 compared to the Boston contract's present value of $28,065,020.

Question 8

An investor deposits $400 into a bank account that earns an annual interest rate of 8%. Based on this information, how much interest will he earn during the second year alone?

Accepted Answer

To calculate the interest earned during the second year, we first need to calculate the interest earned during the first year.

Interest earned during the first year = principal x rate of interest = 400 x 0.08 = $32

At the end of the first year, the total amount in the account will be:

Total amount = principal + interest earned during the first year = 400 + 32 = $432

Now, we need to calculate the interest earned on this new amount during the second year:

Interest earned during the second year = new amount x rate of interest = 432 x 0.08 = $34.56

Therefore, the correct answer is:

Answer: C

Question 9

If a saver has a positive rate of time preference then the present value of $100 to be received 1 year from today is:

Accepted Answer

A positive rate of time preference means that the saver values present consumption more than future consumption. Therefore, the present value of $100 to be received in the future will be less than $100.

Question 10

Suppose Paul borrows $4,000 for one year from his grandfather who charges Paul 7% interest. At the end of the year Paul will have to repay his grandfather:

Accepted Answer

To find how much Paul has to repay after a year, we need to add the interest charged by his grandfather to the original amount borrowed.
Interest = Principal x Rate x Time
Here, Principal = $4,000, Rate = 7% = 0.07, Time = 1 year
Therefore, Interest = $4,000 x 0.07 x 1 = $280
So, the total amount Paul has to repay = $4,000 + $280 = $4,280.
Hence, the answer is A) $4,280.

Question 11

A lender is promised a $100 payment (including interest) one year from today. If the lender has a 6% opportunity cost of money, he/she should be willing to accept what amount today?

Accepted Answer

The correct amount is found by discounting the future payment by the opportunity cost of money, using the formula: Present Value = Future Value / (1 + r)^n, where r is the interest rate and n is the number of periods. Here, it's $100 / (1 + 0.06)^1 = $94.34.

Question 12

The future value of $100 at a 5% per year interest rate at the end of one year is:

Accepted Answer

To calculate the future value of $100 at 5% per year interest rate at the end of one year, we use the formula:
Future Value = Present Value x (1 + interest rate)
= $100 x (1 + 0.05)
= $100 x 1.05
= $105.00
Therefore, the best choice is B, which corresponds to $105.00.

Question 13

Which of the following expresses 5.5%?

Accepted Answer

5.5% is equal to 0.0550 as a decimal, so the best choice is D. A is incorrect because it is too small (just 0.55%). B is incorrect because it has two decimal places and is expressed as a whole number rather than a decimal. C is also incorrect because it is too large (55%).

Question 14

Which of the following best expresses the payment a saver receives for investing their money for two years?

Accepted Answer

The formula for calculating the future value of an investment with compound interest is FV = PV(1 + i)n, where PV is the present value, i is the interest rate, and n is the number of periods. In this case, the investment is for two years, so n = 2. Therefore, the formula for the future value after two years is FV = PV(1 + i)². Since the question is asking for the payment a saver receives, it is assuming that the investment has matured and is being redeemed. Hence, the amount the saver receives is the future value of the investment, which is given by the formula above.

Question 15

Suppose Tom receives a one-year loan from ABC Bank for $5,000.00. At the end of the year, Tom repays $5,400.00 to ABC Bank. Assuming the simple calculation of interest, the interest rate on Tom's loan was:

Accepted Answer

The interest rate is calculated as (Interest / Principal) * 100. Here, the interest is $5,400.00 - $5,000.00 = $400.00. So, the interest rate is ($400 / $5,000) * 100 = 8.00%.

Question 16

Credit:

Accepted Answer

Credit systems have been traced back to ancient civilizations, such as Mesopotamia in 3,000 BCE, which predates the invention of coinage by approximately 2,000 years.

Question 17

Which of the following expresses 5.65%?

Accepted Answer

To express a percentage as a decimal, you must divide it by 100. So, 5.65% divided by 100 is equal to 0.0565. Therefore, the correct answer is D: 0.0565.

Question 18

Which of the following best expresses the payment a lender receives for lending money for three years?

Accepted Answer

The answer of Which of the following best expresses the...

Question 19

Farou invests $2,000 at 8% interest. About how long will it take for Farou to double his investment (e.g., to have $4,000)?

Accepted Answer

Using the Rule of 72, which is a simplified way to estimate the number of years required to double the investment at a fixed annual rate of interest, we divide 72 by the interest rate (8%). 72 / 8 = 9 years.

Question 20

If the interest rate is zero, a promise to receive a $100 payment one year from now is:

Accepted Answer

Even with a zero interest rate, receiving $100 today or one year from now holds the same monetary value. However, due to the potential for inflation or the opportunity cost of not being able to use the money immediately, in practical terms, people might prefer to have the money now. But strictly from a financial calculation standpoint with a 0% interest rate, the present value of receiving $100 one year from now is equal to receiving $100 today.

Quiz 4: Future Value, Present Value and Interest Rates