Question 1

Approximately what rate is needed to double an investment over five years?

Accepted Answer

The formula to calculate the rate needed to double an investment over a given period is:
Rate = (ln 2)/t
Where t is the time in years. 
Substituting t=5 years, we get: 
Rate = (ln 2) / 5 = 0.1386 = 13.86%
So the closest option is C) 14.4%, which is the best choice.

Question 2

Solving for Rates What annual rate of return is earned on a $4,000 investment made in year 2 when it grows to $8,000 by the end of year eight?

Accepted Answer

The correct answer is C.The annual rate of return can be calculated using the formula:r = (FV/PV)^(1/n) - 1where:r = annual rate of returnFV = future valuePV = present valuen = number of yearsIn this case, the present value is $4,000, the future value is $8,000, and the number of years is 8. Plugging these values into the formula, we get:r = (8,000/4,000)^(1/8) - 1r = 1.1225 - 1r = 0.1225Therefore, the annual rate of return is 12.25%.

Question 3

What is the future value of $600 deposited for 4 years earning an 11% interest rate annually?

Accepted Answer

Using the formula for future value of a single sum: 
FV = PV x (1 + r)^n, where 
PV = Present value = $600 
r = Interest rate = 11% or 0.11 (since it's given annually) 
n = Number of years = 4

FV = $600 x (1 + 0.11)^4 
FV = $910.84

Therefore, the future value of $600 deposited for 4 years at an 11% interest rate annually is $910.84, which corresponds to answer choice D.

Question 4

Solving for Rates You invested $1,000 in the stock market one year ago. Today, the investment is valued at $1,250. What return did you earn? What return would you suffer next year for your investment to be valued at the original $1,000?

Accepted Answer

To find the return earned, we can use the formula:

Return = (Ending value - Beginning value) / Beginning value

Return = (1250 - 1000) / 1000 = 0.25 or 25%

To find the return needed for the investment to be valued at the original $1000 next year, we can use the formula:

Beginning value * (1 + Return) = Ending value

1000 * (1 + Return) = 1250

1 + Return = 1.25

Return = 0.25 or 25% decrease, which is equivalent to a 20% loss.

Therefore, the correct answer is A) +25%, -20%, respectively.

Question 5

Solving for Rates You invested $5,000 in the stock market one year ago. Today, the investment is valued at $4,500. What return did you earn? What return would you need to get next year to break even overall?

Accepted Answer

The answer of Solving for Rates You invested $5,000 in...

Question 6

Compute the present value of $3,000 paid in four years using the following discount rates: 3% in year 1, 4% in year 2, 5% in year 3, and 6% in year 4.

Accepted Answer

The answer of Compute the present value of $3,000 paid...

Question 7

General TVM Five years ago, Jane invested $5,000 and locked in an 8 percent annual interest rate for 25 years (end 20 years from now). James can make a twenty year investment today and lock in a 10 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Jane?

Accepted Answer

To solve this problem, we need to use the present value formula of TVM, which is:

PV = FV / (1 + r)^n

Where:
PV = present value
FV = future value
r = interest rate
n = number of periods

First, we need to find out the future value of Jane's investment after 20 years, using the formula:

FV = PV x (1 + r)^n
FV = 5000 x (1 + 0.08)^20
FV = $18,117.52

Next, we need to find out how much James should invest today to have the same future value after 20 years, using the same formula:

PV = FV / (1 + r)^n
PV = 18117.52 / (1 + 0.1)^20
PV = $5,089.91

Therefore, the best choice is C, which is $5,089.91.

Question 8

Determine the interest rate earned on a $800 deposit when $808 is paid back in one year.

Accepted Answer

The interest earned is calculated by subtracting the original deposit from the amount paid back, which is $808 - $800 = $8. The interest rate can be calculated by dividing the interest earned by the original deposit and multiplying by 100 to get a percentage: ($8/$800) x 100 = 1%. Therefore, the answer is choice C.

Question 9

A deposit of $500 earns 5% the first year, 6% the second year and 7% the third year. What would be the third year future value?

Accepted Answer

The correct answer is A because the future value of the deposit after the third year is $595.46. This is calculated by multiplying the initial deposit of $500 by the interest rate for the first year (5%), which gives us $25. This is then added to the initial deposit to give us $525. The interest rate for the second year is 6%, which gives us $31.50. This is added to the previous total to give us $556.50. The interest rate for the third year is 7%, which gives us $38.96. This is added to the previous total to give us $595.46.

Question 10

Solving for Rates What annual rate of return is implied on a $1,000 loan taken next year when $1,500 must be repaid in year 5?

Accepted Answer

To solve for the rate of return, we need to use the formula for compound interest:

Future Value = Present Value x (1 + Rate)^n

where: 
Future Value = $1,500 
Present Value = $1,000 
n = 5 years

We can rearrange the formula to solve for the rate:

Rate = (Future Value / Present Value)^(1/n) - 1

Plugging in the values:

Rate = ($1,500 / $1,000)^(1/5) - 1 
Rate = 1.125^(1/5) - 1 
Rate = 0.1067 or 10.67%

Therefore, the best choice is C.

Question 11

Solving for Rates What annual rate of return is implied on a $700 loan taken next year when $800 must be repaid in year 3?

Accepted Answer

The implied annual rate of return can be calculated using the formula for compound interest: $ FV = PV \times (1 + r)^n $. Here, $ FV = 800 $, $ PV = 700 $, and $ n = 2 $ years. Solving for $ r $, we get $ 800 = 700 \times (1 + r)^2 $. This simplifies to $ (1 + r)^2 = \frac{800}{700} \approx 1.142857 $. Taking the square root gives $ 1 + r \approx 1.069 $, so $ r \approx 0.069 $ or 6.90%.

Question 12

What is the future value of $2,500 deposited for one year earning a 14% interest rate annually?

Accepted Answer

The answer of What is the future value of $2,500...

Question 13

Solving for Rates What annual rate of return is earned on a $2,000 investment made in year 3 when it grows to $3,000 by the end of year six?

Accepted Answer

To solve for the annual rate of return, we can use the following formula:

Ending value = Beginning value x (1 + rate)^n

where:
- Ending value = $3,000
- Beginning value = $2,000
- n = 3 years

Plugging in the values and solving for the rate, we get:

$3,000 = $2,000 x (1 + rate)^3
1.5 = (1 + rate)^3
log(1.5) = log(1 + rate)^3
log(1.5) = 3 log(1 + rate)
log(1 + rate) = log(1.5) / 3
1 + rate = e^(log(1.5) / 3)
rate = e^(log(1.5) / 3) - 1
rate = 14.47%

Therefore, the best choice is B, which corresponds to a rate of 14.47%.

Question 14

What is the present value of a $7,000 payment made in six years when the discount rate is 4%?

Accepted Answer

The present value (PV) is calculated using the formula PV = FV / (1 + r)^n, where FV is the future value ($7,000), r is the discount rate (0.04), and n is the number of years (6). Plugging in the values: PV = 7000 / (1 + 0.04)^6 = 7000 / 1.265319 = $5,532.20.

Question 15

Solving for Rates You invested $5,000 in the stock market one year ago. Today, the investment is valued at $5,500. What return did you earn? What return would you suffer next year for your investment to be valued at the original $5,000?

Accepted Answer

To find the return earned, we use the formula:

Return = (Ending value - Beginning value) / Beginning value

Return = (5500 - 5000) / 5000 = 0.10 or 10%

To find the return needed for the investment to be valued at $5000 again, we need to use the formula:

Ending value = Beginning value + (Return * Beginning value)

5000 = 5500 + (Return * 5500)

-500 = 5500 * Return

Return = -500 / 5500 = -0.0909 or -9.09%

Therefore, the answer is A) 10%, -9.09%, respectively.

Question 16

Compute the present value of $4,000 paid in five years using the following discount rates: 10% in year 1, 2% in year 2, 12% in year 3, and 9% in years 4 and 5.

Accepted Answer

The correct answer is A because the present value of $4,000 paid in five years using the given discount rates is $2,679.15.

Question 17

Approximately how many years does it take to double a $475 investment when interest rates are 8% per year?

Accepted Answer

To solve this problem using the rule of 72: 
72 ÷ interest rate = years to double
So, 72 ÷ 8 = 9
Therefore, it will take approximately 9 years to double the investment at 8% per year.

Question 18

Which is more valuable, receiving $775 today or receiving $885 in two and one-half years if interest rates are 7.25%?

Accepted Answer

The present value of $885 received in 2.5 years at an interest rate of 7.25% is less than $775 today. Calculating the present value: $885 / (1 + 0.0725)^(2.5) ≈ $775. Therefore, $775 today is more valuable.

Question 19

General TVM Ten years ago, Jane invested $1,000 and locked in a 7 percent annual interest rate for 30 years (end 20 years from now). James can made a twenty year investment today and lock in a 6 percent interest rate. How much money should he invest now in order to have the same amount of money in 20 years as Jane?

Accepted Answer

The answer of General TVM Ten years ago, Jane invested...

Question 20

What is the present value of a $600 payment in one year when the discount rate is 8%?

Accepted Answer

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

Quiz 4: Time Value of Money 1: Analyzing Single Cash Flows