Question 1

The monthly mortgage payment on your house is $586.70. It is a 30 year mortgage at a quoted rate of 7.8%. How much did you borrow?

Accepted Answer

The correct answer is D.The monthly mortgage payment can be calculated using the formula:M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)where:M is the monthly mortgage paymentP is the principal (the amount borrowed)r is the monthly interest rate (the quoted rate divided by 12)n is the number of months in the loan termIn this case, we have:M = $586.70r = 7.8% / 12 = 0.0065n = 30 * 12 = 360Substituting these values into the formula, we get:$586.70 = P * (0.0065 * (1 + 0.0065)^360) / ((1 + 0.0065)^360 - 1)Solving for P, we get:P = $81,500Therefore, the amount borrowed is $81,500.

Question 2

What is the future value of $2,400 a year for three years at an 8% rate of interest?

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Question 3

In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the MOST you can withdraw annually?

Accepted Answer

This is a problem that involves calculating the annuity payment from a present value, where the present value is $25,000, the interest rate is 8% per year, and the term is 4 years. The formula for calculating the annuity payment is PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the payment, r is the interest rate per period, and n is the number of periods. Solving for PMT with the given values gives the maximum annual withdrawal closest to option B, $6,988.91.

Question 4

Your firm wants to save $250,000 to buy some new equipment three years from now. The plan is to set aside an equal amount of money on the first day of each year starting today. The firm can earn a 4.7% rate of return. How much does the firm have to save each year to achieve their goal?

Accepted Answer

The correct answer is A.The firm needs to save $75,966.14 each year to achieve their goal. This is calculated using the following formula:PV = FV / (1 + r)^nwhere:PV = present valueFV = future valuer = interest raten = number of yearsIn this case, the firm wants to save $250,000 in three years, so the FV is $250,000. The interest rate is 4.7%, so r = 0.047. The number of years is three, so n = 3.Plugging these values into the formula, we get:PV = $250,000 / (1 + 0.047)^3PV = $250,000 / 1.1525PV = $216,981.13This means that the firm needs to save $216,981.13 today in order to have $250,000 in three years. However, the firm is planning to save an equal amount of money on the first day of each year starting today. So, the amount that the firm needs to save each year is:$216,981.13 / 3 = $75,966.14

Question 5

What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%.

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Question 6

You neighbour makes you the following offer. He will pay you back the money he borrows today over the next 10 years. He will make yearly payments with the first payment being for $1,000 at the end of this year. The payments will grow by 10% every year thereafter. If the appropriate discount rate is 12%, how much would you be willing to lend your neighbour today?

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Question 7

The preferred stock of ABC Co. offers a 10.6% rate of return. The stock is currently priced at $80.19 per share. What is the amount of the annual dividend?

Accepted Answer

The annual dividend can be calculated by multiplying the rate of return (10.6%) by the current price per share ($80.19). So, the calculation is 0.106 * $80.19 = $8.50.

Question 8

If $50,000 is borrowed at an annual interest rate of 8.9% for nine years, determine the annual payments made at the start of each year.

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Question 9

What is the total present value of $50 received in one year, $200 received in two years, and $800 received in six years if the discount rate is 8%?

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Question 10

What is the future value of the following set of cash flows four years from now? Assume an interest rate of 5.5%.

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Question 11

The Government has imposed a fine on the Not-So-Legal Company. The fine calls for annual payments of $100,000, $250,000, and $250,000, respectively over the next three years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including investment earnings, to a national health center. The Government will earn 3.5% on the funds held. How much will the national health center receive three years from today?

Accepted Answer

The future value of each payment is calculated using the formula for future value of a single sum: FV = PV * (1 + r)^n. For the first payment: FV = $100,000 * (1 + 0.035)^2 = $107,122.50. For the second payment: FV = $250,000 * (1 + 0.035)^1 = $258,750. For the third payment: FV = $250,000 (no interest as it's the final year). Adding these gives $107,122.50 + $258,750 + $250,000 = $615,872.50.

Question 12

Your brother-in-law borrowed $2,000 from you four years ago and then disappeared. Yesterday he returned and expressed a desire to pay back the loan, including the interest accrued. Assuming that you had agreed to charge him 10%, and assuming that he wishes to make five equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to pay off the debt? (Assume that the loan continues to accrue interest at 10% per year.)

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Question 13

You are expecting annual cash flows of $80,000 in years 1-5; $95,000 in years 6-20; and $105,000 in years 21-50. If the rate of interest is 10% compounded annually, calculate the present value of this cash flow stream.

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Question 14

A preferred stock pays an annual dividend of $7 a share. The rate of return on this stock is 12.5%. What is one share of this stock worth today?

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Question 15

In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting next year, you plan to withdraw equal amounts from the account at the end of each of the next four years. What is the MOST you can withdraw annually?

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Question 16

Freda Mai has a $65,000 insurance annuity. The company has offered monthly payments for twenty years as a payout option for this annuity. The insurance company will use a 3% rate of return. How much more per month would Freda Mai receive if the insurance company would pay her a 5% rate of return on her annuity?

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Question 17

Moe purchases a $100, 30-year annuity. Larry purchases a $100 perpetuity. In both cases, payments begin in one year, and the appropriate interest rate is 10%. What is the present value of Larry's payments that will occur from year 31 onwards?

Accepted Answer

The present value of a perpetuity starting in year 31 is calculated as the perpetuity value at year 30, discounted back to the present. The perpetuity value at year 30 is $100 / 0.10 = $1000. Discounting this back 30 years at 10% gives $1000 / (1.10)^30 = $57.31.

Question 18

Six years ago, Fred Barnhouse invested $25,000 in old train sets. Four years ago, he invested another $10,000. Last year, he invested an additional $15,000. The train sets have increased in value at a rate of 6.5% annually. What is Fred's investment in these trains worth today?

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Question 19

Mrs. Black established a trust fund that provides $65,000 in scholarships each year for needy students. The trust fund earns a fixed 5.5% rate of return. How much money did Mrs. Black contribute to the fund assuming that only the interest income is distributed?

Accepted Answer

To find the initial contribution, divide the annual scholarship amount by the interest rate (in decimal form). $65,000 / 0.055 = $1,181,818.18.

Question 20

Calculate the present value of a growing annuity given the following information: annual cash flows = $80,000; cash flow growth rate = 3%; required rate of return = 8%; timeframe = 15 years.

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Quiz 6: Discounted Cash Flow Valuation