Engineering Your Future Engineering Economics

18.5 Economics Value and Interest The value of a dollar given to you today is of greater value than that of a dollar given to you one year from today Cash Flow Diagrams Cash Flow Patterns Equivalence of Cash Flow Patterns

Value and Interest “Value” is not synonymous with “amount”. The value of an amount of money depends on when the amount is received or spent.

Value and Interest For example, the promise that you will be given a dollar one year from now is of less value to you than a dollar received today.

Value and Interest The difference between the anticipated amount and its current value is called interest.

Value and Interest What amount must be paid in two years to settle a current debt of $1,000 if the interest rate is 6%?

Cash Flow Diagrams

Cash Flow Patterns

A new widget twister, with a life of six years, would save $2,000 in production costs each year. Using a 12% interest rate, determine the highest price that could be justified for the machine. Although the savings occur continuously throughout each year, follow the usual practice of lumping all amounts at the ends of years.

How soon does money double if it is invested at 8% interest?

Find the value in 2002 of a bond described as “Acme 8% of 2015” if the rate of return set by the market for similar bonds is 10%.

Compute the annual equivalent maintenance costs over a 5-year life of a laser printer that is warranted for two years and has estimated maintenance costs of $100 annually. Use i = 10%.

Unusual Cash Flows and Interest Periods

PAYMENTS AT BEGINNINGS OF YEARS Using a 10% interest rate, find the future equivalent of:

ANNUAL PAYMENTS WITH INTEREST COMPOUNDED m TIMES PER YEAR Compute the effective annual interest rate equivalent to 5% nominal annual interest compounded daily. (There are 365 days in a year.)

CONTINUOUS COMPOUNDING Compute the effective annual interest rate i e equivalent to 5% nominal annual interest compounded continuously.

Your perfectly reliable friend, Frank, asks for a loan and promises to pay back $150 two years from now. If the minimum interest rate you will accept is 8%, what is the maximum amount you will loan him? a) $119 b) $126 c) $129 d) $139 The annual amount of a series of payments to be made at the end of each of the next twelve years is $500. What is the present worth of the payments at 8% interest compounded annually? a) $500 b) $3,768 c) $6,000 d) $6,480

Maintenance expenditures for a structure with a twenty- year life will come as periodic outlays of $1,000 at the end of the fifth year, $2,000 at the end of the tenth year, and $3,500 at the end of the fifteenth year. With interest at 10%, what is the equivalent uniform annual cost of maintenance for the twenty-year period? a) $200 b) $262 c) $300 d) $325 The purchase price of an instrument is $1 2,000 and its estimated maintenance costs are $500 for the first year, $1 500 for the second and $2500 for the third year. After three years of use the instrument is replaced; it has no salvage value. Compute the present equivalent cost of the instrument using 1 0% interest. a) $14,070 b) $15,570 c) $15,730 d) $16,500

If $10,000 is borrowed now at 6% interest, how much will remain to be paid after a $3,000 payment is made four years from now? a) $7,000 b) $9,400 c) $9,625 d) $9,725