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# Micheal wants his \$3,200 to grow to \$4,500 in 3 years. He has a saving account paying simple interest on savings.

Micheal 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?

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:

S=I+I*r*N=I*(1+r*N)

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.

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!

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

NPER = your number of periods
Pmt = skip in this case
PV = your present value, that is the initial investment; make sure to put a minus in front since it's cash outflow
FV = your future value, that is what you're getting back at the end; cash inflow

Hope this helps,
Russ
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