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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?

### 2 Answers by Expert Tutors

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
4.9 4.9 (407 lesson ratings) (407)
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?