Simple interest is calculated solely on the amount initially invested. This calculator can help you deal with many different kinds of simple interest problems. The calculator prints an easy-to-follow, step-by-step explanation.
problem
You deposit some money into a bank account paying 2% simple interest per 6 months. You received $15 in interest after 9 months. How much the deposit (principal) was?
solution
The principal was $500.
explanation
STEP 1: Convert the interest rate of 2% per 6 months into a rate per year.
$$ \text{rate per year = rate per 6 month} \cdot 2 = 2 \% \cdot 2 = 4 \% $$STEP 2: Convert 9 months into years.
$$ \text{ 9 months } = \frac{ 9 }{12} \text{ years} = 0.75 \text{ years}$$STEP 3: Find the principal 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 = $15, i = 4% and t = 0.75 years, so
$$ \begin{aligned} I &= P \cdot i \cdot t \\ P &= \frac{I}{i \cdot t} \\ P &= \frac{ 15 }{ 0.04 \cdot 0.75} \\ \\ P &= 500 \end{aligned}$$Please tell me how can I make this better.