Algebra problem, figuring rate of return.?

Suppose that you invested $16,000 in a high-risk growth fund that after 2 years was worth $25,000. Your broker used the following equation to find the average annual rate of return, (r)

16,000(1 + r)2 = 25,000

What is the annual rate of return?

I don%26#039;t understand the equation.

Algebra problem, figuring rate of return.?

Imagine you have $16000. You put it somewhere for a year, and at the end of it, you get $16000 back. You have the same amount of money at the end as you started with, so you would multiply it by 1.

16,000(1) = 16,000

Now imagine you put it somewhere for a year and get 17,600 back. 17,600 is the initial 16,000 plus an additional 1,600 (10% or 0.1). This 0.1 is r

16,000(1 + r) = 16,000(1 + 0.1) = 16,000(1.1) = 17,600

Now imagine you put that 17,600 back in the fund for another year. You would get 10% of that 17,600 back.

i.e. 17,600(1 + r) = 17,600(1 + 0.1) = 17,600(1.1) = 19,360

So in two years you went from 16,000 to 19,360. This was calculated by:

16,000(1 + r) to get 17,600

17,600(1 + r) to get 19,360

This can be simplified to 16,000(1 + r)(1 + r) or 16,000(1 + r)虏 where the square (虏) shows that the initial amount was put into the fund for 2 years.

So the formula for this example would be 16,000(1 + r)虏 = 19,360

Hopefully the above explained how the formula was derived, so I will use the above figures to walk you through a similar question which you can use as a model for your own calculations.

16,000(1 + r)虏 = 19,360

We want to work out what r is, so we need to leave r on its own.

The first thing to do is to get rid of the 16,000 on the left. So we need to divide both sides by 16,000

(1 + r)虏 = 19,360/16,000

(1 + r)虏 = 1.21

We now need to square root both sides to get rid of the square

1 + r = 鈭?.21

1 + r = 1.1

Then just subtract 1 from each side

r = 1.1 - 1

r = 0.1

r = 10% (rate of return is usually given as a percentage)

which is correct, as can be seen from my initial explanation.

IMPORTANT NOTE: THIS IS NOT THE ANSWER TO YOUR QUESTION. THIS IS SIMPLY A WORKED THROUGH ANSWER OF A SIMILAR QUESTION TO SHOW HOW YOU CAN WORK IT OUT YOURSELF.

Algebra problem, figuring rate of return.?

This is a compound interest problem

A = P(1+r)^n

where P is the amount invested, r is the rate of return of the investment and A is the amount after 2 years

16,000(1 + r)虏 = 25,000

(1 + r)虏 = 25000/16000

(1 + r)虏 = 1.5625

1 + r = 1.25

r = 25%

.

Algebra problem, figuring rate of return.?

Assume that the interest is compounded once a year.

You%26#039;ll have to solve for r.

16000(1+r)(1+r)=25000

(1+r)(1+r)=25000/16000=25/16

1+r+r+r^2=25/16

1+2r+r^2=25/16

multiply both sides by 16

16+32r+16r^2=25

16r^2+32r-9=0

you%26#039;ll have to solve this quadratic equation

ar^2+br+c=0

a=16 b=32 c=-9

r=[-b+-sqrt(b^2-4ac)]/2a

solving r=0.25 or -2.25

r is the rate of return and cannot be negative

so r=0.25 or 1/4 or 4 % per year.

I hope you%26#039;re familiar with this.

Algebra problem, figuring rate of return.?

Let r = annual rate of interest, $16,000 and $25,000 are represented by 16 and 25, respectively.

Finding the rate of interest:

16(1 + r)^2 = 25

4(1 + r) = 5

1 + r = 1.25

r = 0.25

Answer: rate of interest per year is 25%

Proof (determine balances per year after interests are added):

1st year:

= $16,000 + 0.25($16,000)

= $16,000 + $4,000

= $20,000

2nd year:

= $20,000 + 0.25($20,000)

= $20,000 + $5,000

= $25,000

Algebra problem, figuring rate of return.?

16000*(1+r)^2 =25000

(1+r)^2=25000/16000

dividing numerator %26amp; denominator in 1000

(1+r)^2=25/16

taking squareroot on both sides

(1+r) = 5/4

r =5/4 -1

r= 1/4

r=.25

r =25%