Simple interest calculator

problem

You deposit $350 into a bank account, that pays 1.2% simple interest per month. If you received \$9 as interest, find the time for which the money stayed in the bank.

solution

Money stayed in the bank for 2 months and 5 days.

explanation

STEP 1: Convert the interest rate of 1.2% per month into a rate per year.

$$ \text{rate per year = rate per month} \cdot 12 = 1.2 \% \cdot 12 = 14.4 \% $$

STEP 2: Find the time by using the formula $ I = P \cdot i \cdot t $, where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this example I = $9, P = $350 and i = 14.4%, so

$$ \begin{aligned} I &= P \cdot i \cdot t \\ t &= \frac{I}{i \cdot p} \\ t &= \frac{ 9 }{ 0.144 \cdot 350} \\ t &= 0.1786 \text{ years} = \text{ 2 months and 5 days } \end{aligned}$$