EGR310 Homework Week 2

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School

National University *

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Course

310

Subject

Finance

Date

May 16, 2024

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docx

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4

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Homework Set 2 EGR 310 Homework Week 2.Due to Sunday 18,2024 Midnight PST 1. (0.25 pts) $1000 is borrowed for one year at 1.5% per month. If the same amount could be borrowed at 18% per year, how much could be saved? What is the nominal and effective rate for each investment alternative. (Chapter 3) a. 18% per year $1000 x 1.18 = $1180 1.5% per month $1000 x (1 + 0.015)^12 = $1196 $1196 - $1185 = $16 saved at annual rate of 18% Nominal rate 18% Effective rate 1.5% = (1 + 0.015)^12 – 1 = 19.6% 2. (0.25 pts) If you invest $3000 into an account that compounds 7% continuously, what is the annual effective rate? (Chapter 3) a. Effective annual interest rate = ( 1 + 0.07)^12 – 1 1.25% 3. (0.5 pts) You just bought a house for $500,000. You put 20% down and financed the rest over 20 years at 3% nominal interest. Assuming equal monthly payments over the term of the loan, what are the monthly payments? What is the effective rate? (Chapter 4) a. $500,000 x 0.20 = $100,000 down payment, financing $400,000 . Monthly rate is 3%/12 = 0.25% m periods = 12 months x 20 years = 240 Monthly payment = $400,000 x (A/P, 0.25%, 240) = $400,000 x 0.00555 = $2220 month Effective rate = (1 + 0.0025)^12 – 1 = 3.04% 4. (0.5 pts) What would you need to invest today in an account that had a nominal rate of 12% compounded quarterly, if you wanted $9000 in 5 years? What would be the investment required if the account compounded monthly? What is the effective rate of each investment? (Chapter 3) a. F = $9000 i = 12% / 4 quarters = 3% quarterly rate n = 5 years x 4 quarters = 20 interest periods P = $9000 ( P/F, 3%, 20) = $9000 x 0.5537 $4983 Effective rate = (1 + 0.03)^4 – 1 = 12.6% 12% / 12 months = 1% monthly rate n = 5 x (12 months) = 60 interest periods P = $9000 ( P/F, 1%, 60) = $9000 x 0.5504 $4954 Effective rate = (1 + 0.01)^12 – 1 12.7%
5. (0.5 pts) Assume we receive $1200 at the end of each year for 6 years. What is the equivalent value of the cash flows at time period 0 assuming 5% interest? What is the equivalent value at the end of time period 6 assuming 5% interest? (Chapter 4) a. P = A( P/A, 5%, 6) = $1200 (5.076) = $6091 F= A( F/A, 5%, 6) = $1200 (6.802) = $8162 6. (0.5 pts) Assume the following cash flows: (Chapter 4) Assuming an 8% interest rate, what is A? 7. (0.5 pts) The maintenance on a piece of equipment is $800 at the end of year 1 and increases $200/yr each year until the end of the 4 year life of the equipment. Assuming you could invest at 6%, what amount would you need today to cover all the maintenance costs in the future? (Chapter 4) $3485.24 to cover all future maintenance costs.
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