Compounded Interest

Question

A principal amount of $600 earns 3.2% interest compounded monthly. About how long does it take to reach $1000? ROund your answer to the nearest whole number

Answer 1

the underlying formula that you want to use to solve here is

A = P(1 + r/n)^(nt)

for this situation that means first solving for t algebraically and then plugging in the given values

t = ln(A/P) / (n * ln(1 + r/n))

t = ln(1.6667) / 12*ln(1.00267)

t = 0.5108 / 0.0320 = 15.96

meaning that it takes approximately 16 years for the principal amount to reach $1,000

Answer 2

1000= 600(1+.032/12)^12t

solve for t

5/3 = 1.002666...^12t

log_1.002666(5/3) = 12t

12t = ln(5/3)/ln1.002666

t = ln(5/3)/12ln1.002666...

= about 51.9845

= about 52 years