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# Math and Science Solutions for Businesses/Proportions

Question
Hello:

I have determined the solution to the following by using the proportion calculation that follows the question:

If \$1000.00 earns \$250.00 interest in 6 years, how much will earn \$375 in 4 years?

\$375/\$250 = ?/\$1000 (direct proportion)

6 yrs/4 yrs = ?/\$1000 (indirect proportion)

My question is why are the 6 years indirectly proportional to the principal of \$1000?

I can understand how the interest amount of \$250.00 is directly proportional to \$1000 because a larger principal will create a larger interest amount, but how is 6 years indirectly proportional to the principal of \$1000?

Let's examine this question a little more closely. Interest rates and earnings are a little more complicated than just proportions, but let's start off with the approach I think you're trying to use. Let the interest rate for one year be r, then

\$1000･r･(6 years) = \$250.

Solving for r gives r = 250/(1000･6).

If this same r is used for the 2nd calculation, then

new earnings = \$375･r･4 years = 375･(250/(1000･6))･4 = \$62.50

= (375/1000)･(4/6)･250

new earnings = (\$375/\$1000)･(4 years/6 years)･(previous earnings).

So the new earnings are directly proportional to the new principal (\$375) and inversely proportional to the previous earnings (\$1000). Likewise, the new earnings are directly proportional to the new duration (4 years) and inversely proportional to the old duration (6 years).

Your solution of \$2250 is way too high. The lower value makes sense since the principal is smaller and the length of time is shorter.

Interest calculations over different periods (durations) actually take the form

earnings for 1 period = prinicipal･interest rate

Total earnings (original principal, P, plus interest earnings) for n periods = P(1+r)^n

which is more complicated than the calculation above.

Please let me know if this makes sense.

Randy
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply and explantion! I am delighted by the information you provided!

Math and Science Solutions for Businesses

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#### Randy Patton

##### Expertise

Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.

##### Experience

26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

Publications
“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

Education/Credentials
MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

Past/Present Clients
Am also an Expert in Advanced Math and Oceanography