1. To complete your last year in business school and then go through law school,
ID: 2696872 • Letter: 1
Question
1. To complete your last year in business school and then go through law school, you will need $20,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $20,000 one year from today). Your rich uncle offers to put you through school, and he will deposit in a bank paying 4.96% interest a sum of money that is sufficient to provide the 4 payments of $20,000 each. His deposit will be made today.
a.How large must the deposit be? Round your answer to the nearest cent.
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b.How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent.
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c.How much will be in the account immediately after you make the last withdrawal? Round your answer to the nearest cent.
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2.You need to accumulate $10,000. To do so, you plan to make deposits of $1,100 per year - with the first payment being made a year from today - into a bank account that pays 8.63% annual interest. Your last deposit will be less than $1,100 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole.
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b. How large will the last deposit be? Round your answer to the nearest cent.
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3.What is the present value of a perpetuity of $400 per year if the appropriate discount rate is 8.27%? Round your answer to the nearest cent.
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4.If interest rates in general were to double and the appropriate discount rate rose to 16.54%, what would its present value be? Round your answer to the nearest cent.
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5.Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling securities that call for 4 payments of $50 (1 payment at the end of each of the next 4 years) plus an extra payment of $1,000 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $850 each. Your money is now invested in a bank that pays an 10% nominal (quoted) interest rate but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you? Round your answer to the nearest cent.
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6.Assume that your aunt sold her house on December 31, and to help close the sale she took a second mortgage in the amount of $40,000 as part of the payment. The mortgage has a quoted (or nominal) interest rate of 10%, but it calls for payments every 6 months, beginning on June 30, and is to be amortized over 10 years. Now, 1 year later, your aunt must inform the IRS and the person who bought the house about the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) To the closest dollar, what is the total amount of interest that was paid during the first year?
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7.Your company is planning to borrow $1,500,000 on a 7-year, 12%, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal? Round your answer to two decimal places.
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Explanation / Answer
Definition of 'Present Value - PV' The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations. Also referred to as "discounted value". This sounds a bit confusing, but it really isn't. The basis is that receiving $1,000 now is worth more than $1,000 five years from now, because if you got the money now, you could invest it and receive an additional return over the five years. The calculation of discounted or present value is extremely important in many financial calculations. For example, net present value, bond yields, spot rates, and pension obligations all rely on the principle of discounted or present value. Learning how to use a financial calculator to make present value calculations can help you decide whether you should accept a cash rebate, 0% financing on the purchase of a car or to pay points on a mortgage. Definition of 'Future Value - FV' The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. There are two ways to calculate FV: 1) For an asset with simple annual interest: = Original Investment x (1+(interest rate*number of years)) 2) For an asset with interest compounded annually: = Original Investment x ((1+interest rate)^number of years) Consider the following examples: 1) $1000 invested for 5 years with simple annual interest of 10% would have a future value of $1,500.00. 2) $1000 invested for 5 years at 10%, compounded annually has a future value of $1,610.51.
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