Robert P. answered • 08/30/13

All things Math

Barbara R.

asked • 08/30/13Micheal wants his $3,200 to grow to $4,500 in 3 years. He has a saving account paying simple interest on savings. What rate of interest would help him achieve his goal?I am confused as to what formula to use and would you use the banker's rule?

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Robert P. answered • 08/30/13

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All things Math

The key here is understanding that this is SIMPLE INTEREST only (no compound interest). So yes, this would qualify as the banker's rule.

Banker's Rule:

Interest= Principle*Rate*Time

So here, doing the algebra: Rate = Interest / (Principal * Time)

Rate = (4500-3200) / (3200*3)

Rate = 1300 / 9600

Rate = 0.135417

Russell R. answered • 08/30/13

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For me, the simplest way is to use an Excel formula, called **RATE**. But, this is for a **compunded** interest, not the simple one.

Hope this helps,

Russ

Kirill Z. answered • 08/30/13

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If the interest is simple, than it means that it is calculated on the initial deposit, regardless of the number of periods passed.

so, if the initial investment is **I**, interest rate is **r**, and the number of periods is **N**, then the total interest paid will be:

P=**I*****r*****N**

So, if Michael wants his initial investment **I** to grow to certain sum **S**, over **N** periods, the following must be true:

In your problem, **I**=3200; **S**=4500; **N=3**, solve for **r**, multiply result by 100%, this will be the rate which will help him achieve his goal.

Gene G. answered • 08/30/13

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Barbara,

Simple interest uses the formula:

I = prt

where p = the initial principal,

r = the interest rate per unit time

t = time in the units used to express the interest rate.

Your time unit is "year", and the interest rate is annual interest (per year).

Simple interest does not include adding the interest each year. In other words it is not "compound interest". That would make the formula more complex and a little more difficult to solve.

The banker's rule would not apply here. It specifies that the time should be the exact fraction of a year for the time of a loan. (The equation for the interest is the same for a loan or an investment. The only difference is which side of the "loan" you're on.) Your problem states that the time is 3 years, which is just a number of whole years.

The interest to be earned in 3 years is:

4500 - 3200 = 1300

Plug the known values into I = prt and solve for r:

1300 = 3200 * r * 3

1300 = 9600 * r

r = 1300 / 9600

r = 0.1354 = 13.54%

I hope Micheal is patient! He'll probably need more than 3 years!

Lenny D. answered • 01/12/20

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3200 Today compounding at some monthly rate i for 36 months must equal 4200

or 3200*(1+i)^36= 4500 or 4500/3200 = (1+i)^36. take the 35th root of both sides and get = 1.00952 or .952% per month or 11.418% simple annual rate If the deposit only compounded annually we would get (4500/3200)^(1/3 = 1.12035 or annually compounding at 12.035%. Monthly compounding has your interest earning interest earlier.

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