Question 2

Your firm agrees to a contract where you will be paid $50,000 in 9-months when a project is completed. If the discount rate is 6% APR compounded monthly, what is the present value of the contract?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

29595.0000

Incorrect

Q :

2

Suppose the US Treasury starts to issue bonds without maturity, and so would simply pay interest in perpetuity (currently 30 years is the longest maturity length for US Treasury bonds). If the new US bond promised to pay

$50 every 6-months in perpetuity, how much would the bond be worth if similar risk investments yield 3% APR compounded semi-annually?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5343 in box)

Recall that PV_ann = $C/r. If $C is received annually, then r needs to be an annual rate. If $C is received monthly then r needs to be the rate compounded each month, etc

Incorrect

Question 125 / 5 pts

0 / 5 pts

Starting next month, you will deposit $200 per month into an account earning 6% APR compounded monthly. Therefore, my account will reach $500,000 in

years.

(Enter answer in years, rounded to the nearest tenth).

40.1

When solving, we first find the number of months needed to reach the financial goal. Then we can convert that to years by dividing by 12.

Q:3

A client owes the IRS $20,000 in taxes, due today. In lieu of payment today, the IRS will allow your client to make 36 monthly payments of $608.44, with first payment due one month from today. Therefore, the implied interest rate

being charged is2.5% APR compounded monthly.

(Enter the answer as, for example, "4.56" rounded to the nearest basis point, or hundredth of a percent. DO NOT enter the '%' symbol)

Answer 1:

2.5

We need to solve for r in the following equation:

Since there is no closed-form solution, you can solve using a financial calculator, or by trial-an-error. Use a calculator - its much quicker and accurate!

Note that the solution found on your calculator will be a monthly rate (if you enter the number of months in 'N'), so you need to multiply that by 12 to get final answer as an APR.

Question 160 / 5 pts

Starting today, a client will invest $1,000 in your firm's moderate growth fund. He plans to add to this account with annual deposits growing at a rate of 4% per year. How much will he have in 20 years if the fund is expected to earn 8% APR compounded annually? (Assume he makes one final deposit exactly 20 years from today).

Hint: This is a "growing annuity due." Treat as a 20 period growing annuity plus the FV of amount deposited today. Since first deposit today is $1000, the deposit 1-year from today is $1040, etc.

Incorrect

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

66686.0000

You can approach this problem as follows:

First find the PV of cash flows as

, and then find the FV of

that lump sum using r=.08 and t=20 years.

Question 170 / 5 pts

A firm agrees to receive payment from their services as follows: The first of 20 monthly payments of $1000 each will be received 7 months from today. The remaining 19 payments will then immediately follow each month. What is the present value of this contractual agreement if the appropriate discount rate is 6% APR compounded monthly?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

8086.0000

Incorrect

This is a delayed-annuity 20-month annuity with the first payment in 7 months. So, we solve the PV of the 20-month annuity, and then discount it back another 6 months (we do this because the annuity formula as derived assumes the first payment is one period of time ahead). Altogether, we solve:

.

The numerator is the PV of a 20 period $C

annuity at rate r, which we then discount back another 6 periods (because that annuity starts 7 periods from today).

Question 180 / 5 pts

I am currently paying $1,876 in principal and interest on my home loan. Originally this was a 30 year loan with 360 monthly payments, but now I have only 12.5 years of remaining payments (150 payments remain).If I decideto payoff my loan in total today, how much would I owe the bank?Assume my mortgage was financed at 3.69% APR compounded monthly, andassume that there are no prepayment penalties or other fees.

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

281400.0000

The bank would want the present value of the remaining payments they are due to receive! So, this is just a simple present value of an annuity problem.

Incorrect

Question 200 / 5 pts

A client is about to retire at age 62 with a retirement account balance of $3.4 million. You and client decide to invest in a low-risk fund yielding 3% APR compounded monthly. Your client states that they want to receive equal monthly payments (starting one month from today) so that the fund will have zero balance in 30 years (if they live past age 92 then costs will be borne by other assets and social security). What monthly payment will liquidate the account in 30 years at that rate?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

1283.0000

In this case we want to solve for the annuity cash flow that has a PV of 3.4 million at that discount rate.

Incorrect

Question 20 / 5 pts

Your firm agrees to a contract where you will be paid $50,000 in 9-months when a project is completed. If the discount rate is 6% APR compounded monthly, what is the present value of the contract?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

29595.0000

Incorrect

Q :

2

Suppose the US Treasury starts to issue bonds without maturity, and so would simply pay interest in perpetuity (currently 30 years is the longest maturity length for US Treasury bonds). If the new US bond promised to pay

$50 every 6-months in perpetuity, how much would the bond be worth if similar risk investments yield 3% APR compounded semi-annually?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5343 in box)

Recall that PV_ann = $C/r. If $C is received annually, then r needs to be an annual rate. If $C is received monthly then r needs to be the rate compounded each month, etc

Incorrect

Question 125 / 5 pts

0 / 5 pts

Starting next month, you will deposit $200 per month into an account earning 6% APR compounded monthly. Therefore, my account will reach $500,000 in

years.

(Enter answer in years, rounded to the nearest tenth).

40.1

When solving, we first find the number of months needed to reach the financial goal. Then we can convert that to years by dividing by 12.

Q:3

A client owes the IRS $20,000 in taxes, due today. In lieu of payment today, the IRS will allow your client to make 36 monthly payments of $608.44, with first payment due one month from today. Therefore, the implied interest rate

being charged is2.5% APR compounded monthly.

(Enter the answer as, for example, "4.56" rounded to the nearest basis point, or hundredth of a percent. DO NOT enter the '%' symbol)

Answer 1:

2.5

We need to solve for r in the following equation:

Since there is no closed-form solution, you can solve using a financial calculator, or by trial-an-error. Use a calculator - its much quicker and accurate!

Note that the solution found on your calculator will be a monthly rate (if you enter the number of months in 'N'), so you need to multiply that by 12 to get final answer as an APR.

Question 160 / 5 pts

Starting today, a client will invest $1,000 in your firm's moderate growth fund. He plans to add to this account with annual deposits growing at a rate of 4% per year. How much will he have in 20 years if the fund is expected to earn 8% APR compounded annually? (Assume he makes one final deposit exactly 20 years from today).

Hint: This is a "growing annuity due." Treat as a 20 period growing annuity plus the FV of amount deposited today. Since first deposit today is $1000, the deposit 1-year from today is $1040, etc.

Incorrect

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

66686.0000

You can approach this problem as follows:

First find the PV of cash flows as

, and then find the FV of

that lump sum using r=.08 and t=20 years.

Question 170 / 5 pts

A firm agrees to receive payment from their services as follows: The first of 20 monthly payments of $1000 each will be received 7 months from today. The remaining 19 payments will then immediately follow each month. What is the present value of this contractual agreement if the appropriate discount rate is 6% APR compounded monthly?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

8086.0000

Incorrect

This is a delayed-annuity 20-month annuity with the first payment in 7 months. So, we solve the PV of the 20-month annuity, and then discount it back another 6 months (we do this because the annuity formula as derived assumes the first payment is one period of time ahead). Altogether, we solve:

.

The numerator is the PV of a 20 period $C

annuity at rate r, which we then discount back another 6 periods (because that annuity starts 7 periods from today).

Question 180 / 5 pts

I am currently paying $1,876 in principal and interest on my home loan. Originally this was a 30 year loan with 360 monthly payments, but now I have only 12.5 years of remaining payments (150 payments remain).If I decideto payoff my loan in total today, how much would I owe the bank?Assume my mortgage was financed at 3.69% APR compounded monthly, andassume that there are no prepayment penalties or other fees.

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

281400.0000

The bank would want the present value of the remaining payments they are due to receive! So, this is just a simple present value of an annuity problem.

Incorrect

Question 200 / 5 pts

A client is about to retire at age 62 with a retirement account balance of $3.4 million. You and client decide to invest in a low-risk fund yielding 3% APR compounded monthly. Your client states that they want to receive equal monthly payments (starting one month from today) so that the fund will have zero balance in 30 years (if they live past age 92 then costs will be borne by other assets and social security). What monthly payment will liquidate the account in 30 years at that rate?

(Round to the nearest whole dollar. Do not include '$' signs. E.g., if actual solution is $5,343.24, then enter 5,343 in box)

1283.0000

In this case we want to solve for the annuity cash flow that has a PV of 3.4 million at that discount rate.

Incorrect