Financing Word Problem - HELP!

Question

If $350 grows to $500 in 3 years, what is the annual interest rate assuming that interest in compounded annually?

Answer 1

 

350   >>(1+i)>>          >>(1+i)>>         >>>(1+i)>>    500

 

|-----------------|-----------------------|----------------------|

 

time0                1                             2                           3

 

You start w 350 and grows to 500 in 3 yrs. The rate is annual that we will call i

 

so we would have

350 (1+i)^3 = 500

 

(1+i)^3 =500/350

 

(1+i)= (500/350)^(1/3)

 

i= .12624788 (from my phone calculator)

 

And if you plug this value of  i into the original equation it does work

 

Answer 2

The relevant formula for annual compounding is:

 

A = P(1+r)^t

 

Where A is the final amount, P is the initial investment (or deposit), r is the annual percentage rate expressed as a decimal, and t is the number of years.  In your case, we know:

 

A = $500

P = $350

t = 3 years

 

Find r.

 

A = P(1+r)^t

 

A/P = (1+r)^t                        [Divide both sides by P]

 

(A/P)^1/t = 1+r                    [Take the "t"th root (^1/t) of both sides]

 

(A/P)^1/t - 1 = r                   [Subtract 1 from both sides]

 

(500/350)^1/3 - 1 = r          [Plug in values for A=500, P=350, and t=3]

 

Can you finish it from here?