SOLUTION: Austin is going to invest $470 and leave it in an account for 8 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, wou

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Question 1154359: Austin is going to invest $470 and leave it in an account for 8 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Austin to end up with $600?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Eight years is four multiplied by eight quarters or four multiplied by eight compounding periods.

470%281%2Br%29%5E%284%2A8%29=600
(and here, r is for the compounding period, the "quarter".)
Can you solve this?

Answer by ikleyn(52915) About Me  (Show Source):
You can put this solution on YOUR website!
.

600 = 470%2A%281%2Br%2F4%29%5E%284%2A8%29


600%2F470 = %281%2Br%2F4%29%5E32


1+%2B+r%2F4%29%5E32 = 1.276596


Take log base 10 from both sides


    32*log(1+r/4) = log(1.276596)

    log(1 + r/4) = log%28%281.276596%29%29%2F32 = 0.003314

    1+%2B+r%2F4 = 10%5E0.003314 = 1.00766

    r/4 = 1.00766 - 1 = 0.00766

    r = 0.00766*4 = 0.03064 = 3.064% = 3.06% rounded as requested.  ANSWER