Question 1

What's the present value of $1,500 discounted back 5 years if the appropriate interest rate is 6%,compounded semiannually?

Accepted Answer

The answer of What's the present value of $1,500 discounted...

Question 2

At a rate of 6.25%,what is the present value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

Accepted Answer

The answer of At a rate of 6.25%,what is the...

Question 3

What's the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?

Accepted Answer

The perpetuity formula is: PV (present value) = C (annual payment) / r (discount rate). 
In this case, we know that the PV (present value) is $950, and the C (annual payment) is $85. 
Plugging in the numbers, we get: 
$950 = $85 / r 
Solving for r, we get: 
r = $85 / $950 = 0.0895 or 8.95%
Therefore, the rate of return earned is 8.95%. The closest answer choice to this is C.

Question 4

An investment costs $725 and is expected to produce cash flows of $75 at the end of Year 1,$100 at the end of Year 2,$85 at the end of Year 3,and $625 at the end of Year 4.What rate of return would you earn if you bought this investment?

Accepted Answer

The answer of An investment costs $725 and is expected...

Question 5

What annual payment would you have to receive in order to earn a 7.5% rate of return on a perpetuity that has a cost of $1,250?

Accepted Answer

The formula for the present value of a perpetuity is:

PV = A / r

where PV is the present value, A is the annual payment, and r is the discount rate or rate of return.

We are given that the cost (present value) of the perpetuity is $1,250, and we need to find the annual payment required to earn a 7.5% rate of return. Substituting the given values, we get:

$1,250 = A / 0.075

A = $93.75

Therefore, the annual payment required to earn a 7.5% rate of return on a perpetuity that has a cost of $1,250 is $93.75. The best choice is B.

Question 6

By law,credit card issuers must print the annual percentage rate (APR) on their monthly statements.If the APR is stated to be 18.00%,with interest paid monthly,what is the card's EFF percentage?

Accepted Answer

The answer of By law,credit card issuers must print the...

Question 7

An investment costs $1,000 (CF at t = 0) and is expected to produce cash flows of $75 at the end of each of the next 5 years,then an additional lump sum payment of $1,000 at the end of the 5th year.What is the expected rate of return on this investment?

Accepted Answer

The answer of An investment costs $1,000 (CF at t...

Question 8

At a rate of 6.5%,what is the future value of the following cash flow stream: $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

Accepted Answer

The answer of At a rate of 6.5%,what is the...

Question 9

Assume that you own an annuity that will pay you $15,000 per year for 12 years,with the first payment being made today.Your uncle offers to give you $120,000 for the annuity.If you sell it,what rate of return would your uncle earn on his investment?

Accepted Answer

The answer of Assume that you own an annuity that...

Question 10

An investment promises the following cash flow stream: $750 at Time 0; $2,450 at the end of Year 1 (or at t = 1); $3,175 at the end of Year 2; and $4,400 at the end of Year 3.At a discount rate of 8.0%,what is the present value of the cash flow stream?

Accepted Answer

The answer of An investment promises the following cash flow...

Question 11

What's the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%,compounded monthly?

Accepted Answer

The answer of What's the present value of $1,525 discounted...

Question 12

Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the beginning of each year,beginning immediately.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Accepted Answer

To solve this problem, we can use the present value of an annuity formula:

PV = PMT * ((1 - (1/ (1 + r)^n)) / r)

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

We want to solve for n, given that the present value is $25,000, the payment amount is $35,000, and the interest rate is 7.5%.

$25,000 = $35,000 * ((1 - (1/ (1 + 0.075)^n)) / 0.075)

Simplifying this equation gives:

0.7143 = (1 - (1/(1 + 0.075)^n))

Solving for n using logarithms gives:

n = 13.27

Therefore, your uncle can make the $35,000 withdrawals for 13.27 years, and still have $25,000 left in the end. The closest answer choice is C) 13.27.

Question 13

You agree to make 24 deposits of $500 at the beginning of each month into a bank account.At the end of the 24th month,you will have $13,000 in your account.If the bank compounds interest monthly,what nominal annual interest rate will you be earning?

Accepted Answer

The problem describes a scenario of making regular deposits (annuities) at the beginning of each period, which is a case for an annuity due. The future value of an annuity due can be calculated using the formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \times (1 + r)$, where $FV$ is the future value, $P$ is the payment per period, $r$ is the monthly interest rate, and $n$ is the number of periods. In this case, we know the future value ($13,000), the payment per period ($500), and the number of periods (24 months), but we need to find the annual nominal interest rate, which can be found by adjusting the monthly rate found from the equation. Solving this problem requires iteration or financial calculator/computer software because the equation cannot be algebraically rearranged to solve for $r$ directly. Using financial calculation tools, we find that the nominal annual interest rate that matches these conditions is approximately 7.62%.

Question 14

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%,compounded monthly?

Accepted Answer

The formula for future value with monthly compounding is:

FV = P(1 + r/12)^(n*12)

where FV is the future value, P is the initial investment, r is the interest rate (as a decimal), and n is the number of years.

Plugging in the given values, we get:

FV = 1500(1 + 0.06/12)^(5*12)
FV = $2,023.28

Therefore, the best choice is B) $2,023.28

Question 15

What is the present value of the following cash flow stream if the interest rate is 6.0% per year: 0 at Time 0; $1,000 at the end of Year 1; and $2,000 at the end of Years 2,3,and 4?

Accepted Answer

The present value of the cash flow stream is $5,986.81. This is calculated by taking the sum of the present values of each cash flow, which are:* $1,000 / (1 + 0.06)^1 = $943.39* $2,000 / (1 + 0.06)^2 = $1,833.02* $2,000 / (1 + 0.06)^3 = $1,729.63* $2,000 / (1 + 0.06)^4 = $1,620.77Total present value = $943.39 + $1,833.02 + $1,729.63 + $1,620.77 = $5,986.81

Question 16

East Coast Bank offers to lend you $25,000 at a nominal rate of 7.5%,compounded monthly.The loan (principal plus interest) must be repaid at the end of the year.Midwest Bank also offers to lend you the $25,000,but it will charge an annual rate of 8.3%,with no interest due until the end of the year.What is the difference in the effective annual rates charged by the two banks?

Accepted Answer

The answer of East Coast Bank offers to lend you...

Question 17

What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

Accepted Answer

The present value of a perpetuity is calculated using the formula PV = PMT / i, where PV is the present value, PMT is the annual payment, and i is the interest rate. Plugging in the given values, PV = $250 / 0.05 = $5,000.00.

Question 18

Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,beginning at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Accepted Answer

To solve this, we use the formula for the present value of an annuity and the present value of a lump sum. The uncle wants to withdraw $35,000 annually at a 7.5% interest rate and still have $25,000 left. The present value (PV) of the annuity (withdrawals) plus the present value of the lump sum ($25,000) should equal the initial investment ($300,000). The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment, r is the interest rate per period, and n is the number of periods. The present value of the lump sum is calculated as FV / (1 + r)^n, where FV is the future value. By setting up the equation and solving for n, we find that the closest number of years he can make the withdrawals and still have $25,000 left is approximately 14.96 years.

Question 19

What is the present value of the following cash flow stream at an interest rate of 12.0% per year: $0 at Time 0; $1,500 at the end of Year 1; $3,000 at the end of Year 2; $4,500 at the end of Year 3; and $6,000 at the end of Year 4?

Accepted Answer

Using the formula for the present value of an annuity: 
PV = C[(1-(1+r)^-n)/r], where C is the cash flow, r is the interest rate, and n is the number of periods.

PV of Year 1 cash flow = 1500/1.12 = $1,339.29
PV of Year 2 cash flow = 3000/(1.12)^2 = $2,382.35
PV of Year 3 cash flow = 4500/(1.12)^3 = $3,227.67
PV of Year 4 cash flow = 6000/(1.12)^4 = $4,797.67

Total PV = $1,339.29 + $2,382.35 + $3,227.67 + $4,797.67 = $10,746.99.

Therefore, the best choice is B.

Question 20

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%,compounded semiannually?

Accepted Answer

The future value is calculated using the formula FV = P(1 + r/n)^(nt), where P = $1,500, r = 0.06, n = 2 (semiannual compounding), and t = 5 years. Plugging in these values, FV = 1500(1 + 0.06/2)^(2*5) = 1500(1.03)^10 = $2,015.87.

Quiz 4: Time Value of Money