Starting next year, you will need $5,000 annually for 4 years to complete your education. (One year from today you will withdraw the first$5,000.) Your uncle deposits an amount today in a bank paying 6% annual interest, which will provide the needed $5,000 payments. a. How large must the deposit be? b. How much will be in the account immediately after you make the first withdrawal?

Starting next year, you will need $\$ 10,000$ annually for $4$ years to complete your education. (One year from today you will withdraw the first $\$ 10,000$.) Your uncle deposits an amount today in a bank paying $5 \%$ annual interest, which will provide the needed $\$ 10,000$ payments.

a. How large must the deposit be?

b. How much will be in the account immediately after you make the first withdrawal?

As a jewelry store manager, you want to offer credit, with interest on outstanding balances paid monthly. To carry receivables, you must borrow funds from your bank at a nominal 9%, monthly compounding. To offset your overhead, you want to charge your customers an EAR (or EFF%) that is 3% more than the bank is charging you. What APR rate should you charge your customers?

Your firm sells for cash only, but it is thinking of offering credit, allowing customers 90 days to pay. Customers understand the time value of money, so they would all wait and pay on the 90th day. To carry these receivables, you would have to borrow funds from your bank at a nominal 9%,daily compounding based on a 360-day year.You want to increase your base prices by exactly enough to offset your bank interest cost. To the closest whole percentage point, by how much should you raise your product prices?

You want to buy a house within 3 years, and you are currently saving for the down payment. You plan to save $9,000 at the end of the first year, and you anticipate that your annual savings will increase by 5% annually thereafter. Your expected annual return is 8%. How much will you have for a down payment at the end of Year 3?

You have saved $4,000 for a down payment on a new car. The largest monthly payment you can afford is$350. The loan will have a 12% APR based on end-of-month payments. What is the most expensive car you can afford if you finance it for 48 months? For 60 months?

a. Find the present values of the following cash flow streams at a 5% discount rate.

$$\begin{matrix} \text{ } & \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \text{Stream A} & \text{\$ 0} & \text{\$ 150} & \text{\$ 450} & \text{\$ 450} & \text{\$ 450} & \text{\$ 250}\\ \text{Stream B} & \text{\$ 0} & \text{\$ 250} & \text{\$ 450} & \text{\$ 450} & \text{\$ 450} & \text{\$ 150}\\ \end{matrix}$$

b. What are the PVs of the streams at a 0% discount rate?

Find the future values of the following ordinary annuities: a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. b. FV of$200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly. c. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

An investment will pay $150 at the end of each of the next 3 years,$250 at the end of Year 4, $300 at the end of Year 5, and$500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value?

Your client is 26 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $8,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 10% in the future. a. If she follows your advice, how much money will she have at 65? b. How much will she have at 70? c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to earn the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age?

Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How much repayment of principal was included? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year? d. If the payments are constant, why does the amount of interest income change over time?

Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $62 million, to receive 10 end-of-year payments of$9.5 million, or to receive 30 end-of-year payments of $5.6 million. a. If she thinks she can earn 7% annually, which should she choose? b. If she expects to earn 8% annually, which is the best choice? c. If she expects to earn 9% annually, which option would you recommend? d. Explain how interest rates influence her choice.

What role do interest rates play in allocating capital to different potential borrowers?

Investigate the difference between compounding annually and simple interest. Find the simple interest for a three-year CD for $5,000 at an interest rate of 6%.