Pre Calculus 12 Finance-Investing money

Question

If John inherited $200000 and wanted to grow it into $500000 in 25 years, what rate of annual interest compounded monthly would he need to earn his goal? Solve algebraically.

Answer 1

50000 = 20000(1 + r/12)^(12)(25)

2.5 = (1 + r/12)³⁰⁰

ln 2.5 = 300 ln (1 + r/12)

0.91629 = 300 ln (1 + r/12)

0.00930543 = ln (1 + r/12))

e^0.00930543 = 1 + r/12

1.003058972 = 1 + r/12

0.003048972 = r/12

0.0367 = r