Question

For how long must $700 be left on deposit at 6% compounded monthly to reach a total accumulation of $1750?

(Note: I know how to find this with a calculator, I would like to see the mechanic of how LN would be used to solve this...thanks)

Answer 1

your job is to solve
\[700(1+\frac{.06}{12})^{12t}=1750\] for t

Answer 2

or
\[700(1.005)^{12t}=1750\] divide by 700 get
\[(1.005)^{12t}=2.5\] then using logs get
\[12t=\frac{\ln(2.5)}{\ln(1.005)}\] or
\[t=\frac{\ln(2.5)}{12\ln(1.005)}\]now you really need a calculator, because you cannot do this with arithmetic