How many years will it take $2,000 invested at 6% to earn $360?

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Answer 1 · 2017-12-23T09:17:31

3 years

In one year, yo can earn $120.
Just multiply $120 by 6% to get it.

Then divide $360 by $120.
The answer is 3.

Therefore, it will take 3 years to earn $360.

Answer 2 · 2017-12-23T09:24:17

Will take 3 years

Im guessing you mean there is an annual interest of $6%$

We can use the formula for compound interest...

$A = N_0 ( 1 + P/100 ) ^t$

$N_0$ - Initial amound

$P$ - percentage

$t$ - time in years

For us to earn $$360$ it would mean to have $$2,360$ in the account after $t$ years

$=> 2360 = 2000*(1+6/100)^t$

Dividing by $2000$ and simplifying...

$=> 59/50 = (53/50)^t$

Taking $log_10$ to both sides:

$=> log (59/50) = log (53/50)^t$

Using our log laws:

$logalpha^beta -= betalogalpha$

$=>log(59/50) = t*log(53/50)$

$=> t = log(59/50) / log(53/50)$

$=> t approx 2.841$ years

$=> t = 3$ years