Question

1. Valley Rendering, Inc. is considering purchasing a new flotation system for recovering more grease. The company can finance a $150,000 system at 5% per year compound interest or 5.5% per year simple interest. If the total amount owed is due in a single payment at the end of 3 years, (a) which interest rate should the company select, and (b) how much is the difference in interest between the two schemes? (ANSWER: (b) $1106.) 2. A mechanical consulting company is examining its cash flow requirements for the next 7 years. The company expects to replace office machines and computer equipment at various times over the 7-year planning period. Specifically, the company expects to spend $7000 two years from now, $9000 t five years from now. What is expenditures at an interest rate of 10% per year? (ANSWER: $15651) three years from now, and S5000 the present worth of the planned 3. A green algae, chlamydomonas reinhardtii, can produce hydrogen when temporarily deprived of sulfur for up to two days at a time. How much could a small company afford to spend now to commercialize the process if the net value of the hydrogen produced is $280,000 per year? Assume the company wants to earn a rate of return of 18% per year and recover its investment in 8 years. (ANSWER: $1,141,728) 4. A concept car that will get 100 miles per gallon and carry 4 persons would have a carbon-fiber and aluminium composite frame with a 900 cc three cylinder turbodieselVelectric hybrid power plant. The extra cost of these technologies is estimated to be S11,000. If gasoline savings over a comparable conventional car would be $900 in year 1, increasing by 10% each year, what is the present worth of the savings over a 10-year period at an interest rate of 8% per year? (ANSWER: $9063.21) 5. Shifted cash flow: Revenue from gas wells that have been in production for at least 5 years tends to follow a decreasing geometric gradient. One particular rights holder received royalties of $4000 per year for years through 6 (i.e. six times), but beginning in year 7, income decreased by 15% per year through year 14 (geometric gradient of 15%). What was the future value (year 14) of the income from the well, ifall of the income was invested at 10% per year? (ANSWER: $91,601)

Answer 1

Question 1

(a)

Case I - Compound Interest

Sum borrowed = $150,000

Interest rate = 5% per annum

Time period = 3 years

Calculate the amount to be repaid -

Amount = Sum borrowed * (1 + interest rate)^{Time period}

Amount = $150,000 * (1+0.05)³

Amount = $150,000 * (1.05)³

Amount = $150,000 * 1.157625

Amount = $173,644

The amount to be repaid in case of compound interest rate scheme is $173,644.

Case II - Simple Interest

Sum borrowed = $150,000

Interest rate = 5.5% or 0.055

Time period = 3 years

Calculate the simple interest -

Simple interest = Sum borrowed * Interest rate * Time period

Simple interest = $150,000 * 0.055 * 3 = $24,750

Amount to be repaid = Sum borrowed + Simple interest

Amount to be repaid = $150,000 + $24,750 = $174,750

The amount to be repaid in case of simple interest rate scheme is $174,750

Amount to be repaid is less in case of compound interest.

So,

The company should select 5% per year compound interest.

(b)

Calculate the compound interest paid -

Compound interest paid = Amount repaid - Sum borrowed = $173,644 - $150,000 = $23,644

Calculate the difference in interest -

Difference in interest = Simple interest paid - Compound interest paid

Difference in interest = $24,750 - $23,644 = $1106

Thus,

The difference in interest between the two schemes is $1106.