Question 1

Moving Cash Flows What is the value in year 7 of a $700 cash flow made in year 3 when the interest rates are 10 percent?

Accepted Answer

To move cash flows, we use the formula: PV = FV / (1 + r)^n
In this case, n = 4 (7-3), r = 10%, and FV = $700.
So, PV = $700 / (1 + 0.10)^4 = $478.11
Therefore, the value in year 7 of a $700 cash flow made in year 3 when the interest rates are 10 percent is $1,024.87 (FV of $478.11 moved forward four years).

Question 2

Solving for Rates What annual rate of return is earned on a $200 investment when it grows to $850 in ten years?

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Question 3

Solving for Rates What annual rate of return is earned on a $10,000 investment when it grows to $15,000 in ten years?

Accepted Answer

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

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

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

Plugging in the given information, we get:

$15,000 = $10,000(1 + r/1)^(1 x 10)

Simplifying:

1.5 = (1 + r)^10

Taking the 10th root of both sides:

1 + r = 1.0414

Subtracting 1 from both sides:

r = 0.0414 = 4.14%

Therefore, the correct answer is C) 4.14%.

Question 4

Interest-on-Interest Consider a $200 deposit earning 8 percent interest per year for 3 years. How much total interest is earned on interest (excluding interest earned on the original deposit)?

Accepted Answer

The total interest earned on interest is calculated by finding the compound interest and subtracting the simple interest. The compound interest for 3 years is $200 * (1.08)^3 - $200 = $51.94. The simple interest for 3 years is $200 * 0.08 * 3 = $48. The interest on interest is $51.94 - $48 = $3.94.

Question 5

Moving Cash Flows What is the value in year 3 of a $500 cash flow made in year 5 when interest rates are 6 percent?

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Question 6

Solving for Rates What annual rate of return is earned on a $900 investment when it grows to $2,500 in fifteen years?

Accepted Answer

To solve for the annual rate of return, we can use the formula: 
Final value = initial value x (1 + r)^n 
where r is the annual rate of return, n is the number of years, and we are given the final value ($2,500) and initial value ($900).

Therefore, we can plug in the values: 
$2,500 = $900 x (1 + r)^15

Dividing both sides by $900: 
2.7777778 = (1 + r)^15

Taking the 15th root: 
1.0705321 = 1 + r

Subtracting 1 from both sides: 
r = 0.0705321 = 7.05321%

Rounding to two decimal places, the answer is 7.05%. Therefore, the best choice is D.

Question 7

Future Value At age 20 you invest $1,000 that earns 7 percent each year. At age 30 you invest $1,000 that earns 10 percent per year. In which case would you have more money at age 60?

Accepted Answer

Investing the $1,000 at a higher rate of return (10 percent) for a longer time period (30 years) will result in a higher future value at age 60 compared to investing $1,000 at 7 percent for only 10 years.

Question 8

Solving for Time How many years will it take $1 million to grow to $3 million with an annual interest rate of 7 percent?

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Question 9

Future Value At age 25 you invest $2,000 that earns 6 percent each year. At age 35 you invest $2,000 that earns 9 percent per year. In which case would you have more money at age 60?

Accepted Answer

To calculate the future value at age 60, we need to use the formula for compound interest:

FV = PV × (1 + r)n

where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.

For option A, the future value at age 60 can be calculated as:

FV = 2,000 × (1 + 0.06)35 = $14,974.73

For option B, the future value at age 60 can be calculated as:

FV = 2,000 × (1 + 0.09)25 × (1 + 0.06)10 = $21,266.14

Therefore, option B yields more money at age 60 than option A.

Question 10

Solving for Time How long will it take $100 to reach $500 when it grows at 10 percent per year?

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Question 11

Moving Cash Flows What is the value in year 6 of a $900 cash flow made in year 4 when the interest rates are 8 percent?

Accepted Answer

To move a cash flow two years forward, we need to compound it once by the interest rate for the first year and then compound the result again by the interest rate for the second year. 
So, to move a cash flow from year 4 to year 6, we compound it twice as follows:

FV = $900 x (1 + 0.08)² 
FV = $1,049.76

Therefore, the value of the $900 cash flow in year 6 at an interest rate of 8% is $1,049.76.

Question 12

Solving for Time How long will it take $3,000 to reach $5,000 when it grows at 7 percent per year?

Accepted Answer

We can use the formula for compound interest:

FV = PV*(1+r)^n

where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years.

Plugging in the values we know:

5000 = 3000*(1+0.07)^n

Dividing both sides by 3000:

1.66666667 = (1.07)^n

Taking the natural log of both sides:

ln(1.66666667) = n*ln(1.07)

Dividing both sides by ln(1.07):

n = ln(1.66666667)/ln(1.07) = 7.55 years (rounded to two decimal places)

Therefore, the best choice is B.

Question 13

Solving for Time How many years will it take $100 to grow to $1,000 with an annual interest rate of 8 percent?

Accepted Answer

We can solve for time using the formula:
future value = present value x (1 + interest rate)^time
Substituting the given values, we get:
1000 = 100 x (1 + 0.08)^time
Simplifying this equation, we get:
10 = (1.08)^time
Taking the logarithm of both sides, we get:
log 10 = log (1.08)^time
log 10 = time x log 1.08
Solving for time, we get:
time = log 10 / log 1.08
time = 29.92 years (rounded to two decimal places)
Therefore, the best choice is C.

Question 14

Solving for Time How long will it take $4,000 to reach $4,500 when it grows at 8 percent per year?

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Question 15

Solving for Rates You invested $1,000 in the stock market one year ago. Today, the investment is valued at $750. What return did you earn? What return would you need to get next year to break even overall?

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Question 16

Solving for Rates What annual rate of return is earned on a $5,000 investment when it grows to $7,000 in six years?

Accepted Answer

To calculate the annual rate of return, we can use the formula: 
(Ending value / Beginning value)^(1/number of years) - 1

Plugging in the values given, we get: 
(7000 / 5000)^(1/6) - 1 = 0.0577 or 5.77%

Therefore, the correct answer is choice C - 5.77%.

Question 17

Solving for Time How many years will it take $200 to grow to $250 with an annual interest rate of 4 percent?

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Question 18

Moving Cash Flows What is the value in year 3 of a $250 cash flow made in year 15 when interest rates are 12 percent?

Accepted Answer

To move a cash flow from year 15 to year 3, we need to discount the cash flow by 12% for 12 years (from year 15 to year 3). 
PV = FV / (1 + r)^n 
PV = $250 / (1 + 0.12)^12 
PV = $64.17

Question 19

Moving Cash Flows What is the value in year 5 of a $600 cash flow made in year 10 when interest rates are 5 percent?

Accepted Answer

To calculate the value of a cash flow made in the future, we need to discount it back to the present using the formula:

Present Value = Future Value / (1 + r)n

Where r is the interest rate and n is the number of years.

In this case, we need to find the present value of a $600 cash flow made in year 10 when interest rates are 5 percent, 5 years from now (in year 5). So, we have:

Present Value = $600 / (1 + 0.05)5
Present Value = $470.12

Therefore, the value of the $600 cash flow made in year 10, when interest rates are 5 percent, 5 years from now (in year 5) is $470.12. The correct choice is C.

Question 20

Moving Cash Flows What is the value in year 15 of a $600 cash flow made in year 3 when the interest rates are 4 percent?

Accepted Answer

To find the FV of a cash flow that occurs earlier than the ending year, we use the formula:

FV = CF x (1 + r)^n

where CF is the cash flow, r is the interest rate, and n is the number of years between the cash flow and the ending year.

In this case, the cash flow of $600 occurs in year 3, and we want to find its value in year 15. So, n = 15 - 3 = 12.

Plugging in the values:

FV = 600 x (1 + 0.04)^12 
FV = 960.62

Therefore, the value of the cash flow in year 15 is $960.62.

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