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Financing Word Problem - HELP!

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

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Brett K. | Experienced Math and Spanish TutorExperienced Math and Spanish Tutor
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
 
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (438 lesson ratings) (438)
1
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?