Simple interest calculator

problem

You deposit $12000 into a bank account, that pays 1.5% simple interest per month. You left the money in there for 210 days. Determine the interest earned and the total amount at the end of those 210 days.

solution

The interest is $1242.734 and the amount is $13242.734.

explanation

STEP 1: Convert the interest rate of 1.5% per month into a rate per year.

$$ \text{rate per year = rate per month} \cdot 12 = 1.5 \% \cdot 12 = 18 \% $$

STEP 2: Convert 210 days into years.

$$ \text{ 210 days } = \frac{ 210 }{365} \text{ years} = 0.57534 \text{ years}$$

STEP 3: Find the interest 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 examplee P = $12000, i = 18% and t = 0.57534 years, so

$$ \begin{aligned} I &= P \cdot i \cdot t \\ I &= 12000 \cdot 0.18 \cdot 0.57534 \\ I &= 1242.734 \end{aligned}$$

STEP 4: Find the amount by using the formula $ A = P + I $.

Since P = $12000 and I = $1242.734 we have

$$ \begin{aligned} A &= P + I \\ A &= 12000 + 1242.734 \\ A &= 13242.734 \end{aligned} $$