Math and Science Solutions for Businesses/Simple Interest

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Question
QUESTION: Hello:

The simple interest calculation is as follows:

P X R X T = interest

Here is an example:

$600 X 6% X 60/360. I am using 360 days as the days in a year for this calculation.

Now the 6% is the annual rate; so I assume that it can be expressed as 6%/year.

So, now the calculation appears as $600 X 6%/year X time.

The time is expressed as 60 days or 60/360. I believe that 60/360 represents a fractional part of one year; so the calculation is now $600. X 6%/year X (60/360) year. I think that this is correct, but I'm not totally sure. The "years" cancel from the calculation.

The calculation, I think, can use days instead of years.

$600 X 6%/(360 days) X 60 days = $6.00 The "days" cancel from the calculation.

I think the following calculation is not correct: $600 X 6%/(360 days) X 60/360 year. There are two "360" that will prevent the calculation from providing the correct answer.

So, my question is as follows: Are 1. and 2. below correct and is 3. incorrect?

1. $600 X 6%/year X (60/360) year = $6.00

2. $600 X 6%/(360 days) X 60 day = $6.00

3. $600 X 6%/(360 days) X 60/360 year = $0.016666...

I thank you for your reply.

ANSWER: #s 1. and 2. are correct.

The way I think of this is, given the principal P = $600, R = annual interest rate and T = time after the principal starts compounding (T = 0, i.e, right away), then

Interest = P・R・(fraction of year).

It looks like fraction of year you are interested in is 60 days/360 days = 0.167, so

I = P・R・(60/360).

As your solutions 1. and 2. indicate, you can use the fraction of the year that the interest rate has been working on the principal (#1) or the fraction of the interest rate R that corresponds to 60 days, R/360 (#2). I prefer the 1st way, but whatever.

Let me know if this makes sense.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for your reply!

Yes, your reply makes sense to me.  I do have one other calculation that I do not understand why it is incorrect.  It is similar to my 2. calculation.

$600 X 6%/(360 days/year) X 60 days = the "years" need to cancel or the answer is 6.00 dollar years or $6.00 years, if I'm not mistaken. This calculation is incorrect, but I do not know why.

I used years in 360 because there are 360 days in a so called banker's year.

I thank you for your follow-up reply.

Answer
I'm not sure why you say the calculation is incorrect. Did you take into account that 6% really means the fraction 0.06? Also, just to be a little more rigorous (and to make sure we are on the same page), you should precisely define the terms and variables you are using. Eg., T =  a fraction, with no units, not years or days or any other unit of time. Are you being consistent with your units?

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Randy Patton

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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.

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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.

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

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

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