Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $125 annually if the next payment occurs one year from today? The market interest rate is 3.9 percent.

Present Value and Multiple Cash Flows Wilkinson Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, 1) what is the present value of these cash flows? 2) What is the future value of these cash flows at the end of year 4? 3) What is the present value at 18 percent?

Year	Cash Flow
1	$ 675
2	880
3	985
4	1,530

Present Value and Multiple Cash Flows Investment X offers to pay you $3,900 per year for nine years, whereas Investment Y offers to pay you $6,100 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent?

Calculating Annuity Present Value An investment offers $5,650 per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?

Calculating EAR Find the EAR in each of the following cases:

APR	Number of Times Compounded	EAR
6.70%	Quarterly
12.4	Monthly
9.8	Daily
8.4	Infinite

Calculating EAR First National Bank charges 10.3 percent compounded monthly on its business loans. First United Bank charges 10.5 percent compounded semiannually. As a potential borrower, to which bank would you go for a new loan?

[Hint: You will select a bank that provides you a higher or lower EAR? Note that you are the borrower.]

Future Value What is the future value in six years of $1,000 invested in an account with an APR of 7.5 percent,

[Hint: Compute EAR and then you can use FV lump sum formula to estimate future value FV = PV*(1 + i)ⁿ, where you plug in your EAR as i. ]

Compounded annually?

Compounded semiannually?

BGN/END Modes An investment offers the following cash flows: $2,000 per year for four years starting from year 2 to year 5 (annual payment). Assume APR is 8% and interest is compounded annually. You may use BGN or END modes to solve these questions. (Please specify which mode you are in.)

What is the value of this investment at time t =1 (PV₁)?

PV₀?

FV₅?

FV₆?

FV₇?

An interest is stated as 16% APR compounded quarterly. Find the following effective interest rates:

Effective monthly rate, (b) effective quarterly rate, and (c) effective annual rate.

An interest is stated as 24% APR compounded monthly. Find the following effective interest rates:

Effective monthly rate, (b) effective quarterly rate, and (c) effective annual rate.

An investment offers nothing in months 1-3, then $650 every month from month 4 to month 10. The interest rate available to you is 16% per year (i.e., APR = 16%) and interest is compounded quarterly.

Draw a timeline for these cash flows.

Compute the relevant effective interest rate for your cash flow analysis.

How much are you willing to pay for the investment today.

Calculating Rates of Return Youre trying to choose between two different investments, both of which have up-front costs of $75,000. Investment G returns $125,000 in six years. Investment H returns $185,000 in 10 years. Which of these investments has the higher return? Which investment would you choose?

Growing Annuity Your job pays you only once a year for all the work you did over the previous 12 months. Today, December 31, you just received your salary of $72,500, and you plan to spend all of it. However, you want to start saving for retirement beginning next year. You have decided that one year from today you will begin depositing 5 percent of your annual salary in an account that will earn 9 percent per year. Your salary will increase at 3.7 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?

[Hint: Try to draw a timeline. 1)What will be your salary at year 1 if you just received your salary of $72,500 (at time t = 0)? 2) How much are you saving in year 1? 3) You may want to compute PV of annuity first using the growing annuity formula and then try to compute FV using lump sum formula.]

Present and Future Values The present value of the following cash flow stream is $7,300 when discounted at 7.1 percent annually. What is the value of the missing cash flow?

[Hint: you may approach this question using PV of lump sum formula, discount individual cash flow one-by-one; PV = FV/(1+i)ⁿ]

Year	Cash Flow
1	$1,500
2	?
3	2,700
4	2,900

Amortization with Equal Payments. Prepare an amortization schedule for a three-year loan of $54,000. The interest rate is 8% per year, ant the loan calls for equal annual payments. How much interest is paid in the third year? How much total interest is paid over the life of the loan?