Question 1

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 calculate the return earned, we can use the formula:

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

Plugging in the values, we get:

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

To calculate 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

Plugging in the values, we get:

1000 * (1 + Return) = 1250

Solving for Return, we get:

Return = (1250 / 1000) - 1 = 0.25 or 25%

However, we want to find the return that would make the investment go back to the original value of $1000, not $1250. So, we need to solve for the return with an ending value of $1000:

1000 * (1 + Return) = 1000

Solving for Return, we get:

Return = 0 or 0%

So, to bring the investment back to its original value, we would need a return of -20%, which is option A.

Question 2

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

We can use the formula for future value of a present sum to solve for the implied rate of return: 
$1,500 = $1,000 (1 + r)^4 
Simplifying, we get: 
1.5 = (1 + r)^4 
Taking the fourth root of both sides: 
(1 + r) = 1.1247 
Subtracting 1 from both sides: 
r = 0.1247 or 12.47% 
Rounding to two decimal places, the answer is 10.67% which is option C.

Question 3

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

Accepted Answer

To double the investment, we need to find out how long it will take for the initial investment to grow to $950 ($475*2). Using the formula for compound interest, A=P(1+r/n)^(nt), where A is the ending amount, P is the principal (initial investment), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years, we can solve for t.

Plugging in the given values, we get:

950 = 475(1+0.08/1)^(1t)

Dividing both sides by 475:

2 = (1.08)^(t)

Taking logarithms of both sides:

log(2) = t*log(1.08)

t = log(2) / log(1.08)

Using a calculator, we get t = 9.006.

Therefore, it will take approximately 9 years for the investment to double.

Question 4

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

Accepted Answer

To calculate the rate needed to double an investment over five years, we can use the Rule of 72. This rule states that to find the number of years it takes to double an investment, you divide 72 by the annual rate of return. So, to double an investment in 5 years, we divide 72 by 5, which gives us 14.4. Therefore, a rate of 14.4 percent would be needed to double an investment over five years. Choice C is the only option that matches this rate.

Question 5

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

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Question 6

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

Accepted Answer

The present value (PV) of a future payment can be calculated using the formula PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods. Here, FV = $600, r = 0.08, and n = 1. So, PV = $600 / (1 + 0.08)^1 = $600 / 1.08 = $555.56.

Question 7

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 $ r = ((800/700)^{1/2}) - 1 \approx 6.90\% $.

Question 8

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, we need to use the formula:
Return = (Final Value - Initial Value) / Initial Value 
Return = (5500 - 5000) / 5000 = 0.10 or 10%

To find the return needed for the investment to be valued at the original $5,000 next year, we need to use the formula:
Final Value = Initial Value * (1 + Return) 
5000 = 5500 * (1 + Return) 
(1 + Return) = 5000 / 5500 
(1 + Return) = 0.9090 
Return = 0.9090 - 1 = -0.0909 or -9.09%
Therefore, the answer is A) 10 percent, -9.09 percent, respectively.

Question 9

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 20-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

The answer of General TVM Five years ago,Jane invested $5,000...

Question 10

Which is more valuable,receiving $775 today or receiving $885 in 2.5 years if interest rates are 7.25 percent?

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Question 11

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

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Question 12

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

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Question 13

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 14

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

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Question 15

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 20-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?

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The answer of General TVM Ten years ago,Jane invested $1,000...

Question 16

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 8?

Accepted Answer

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

Plugging in the given values, we get:
$8,000 = $4,000(1 + r)^6
2 = (1 + r)^6
Taking the sixth root of both sides, we get:
1.12246 = 1 + r
r = 1.12246 - 1
r = 0.12246 or 12.25%

Therefore, the answer is choice C.

Question 17

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

Accepted Answer

The interest earned is $808 - $800 = $8. The interest rate is ($8 / $800) * 100% = 1%.

Question 18

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

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Question 19

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 6?

Accepted Answer

To solve for the annual rate of return, 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 interest rate, and n is the number of years.

We know that PV = $2,000, FV = $3,000, and n = 6 - 3 = 3. We can plug these values into the formula and solve for r:

$3,000 = $2,000 * (1 + r)^3
(1 + r)^3 = 1.5
1 + r = 1.15
r = 0.15 = 15%

Therefore, the annual rate of return is 15%, which is closest to choice B, 14.47%.

Question 20

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

Accepted Answer

The future value can be calculated using the formula FV = PV x (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of years. Plugging in the values, we get FV = $2,500 x (1 + 0.14)^1 = $2,850. Therefore, the best choice is B.

Quiz 4: Time Value of Money