Compound interest is calculated on both the initial payment and the interest earned in previous periods.
problem
If you deposit $3500 into an account paying 10% annual interest compounded monthly. Find the amount and interest after 8 years?
solution
The amount is $7763.37 and the interest is $4263.37.
explanation
STEP 1: To find amount we use formula:
$$ A = P \left( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}} $$ |
A = total amount P = principal (amount of money deposited) r = annual interest rate n = number of times compounded per year t = time in years |
In this example we have
$$ P = \$3500 ~,~ r = 10 \% ~ , ~ n = 12 ~ \text{and} ~ t = 8 ~ \text{years}$$After plugging the given information we have
$$ \begin{aligned} A &= 3500 \left( 1 + \frac{ 0.1 }{ 12 } \right)^{\Large{ 12 \cdot 8 }} \\ A &= 3500 \cdot { 1.008333 } ^ { 96 } \\ A &= 3500 \cdot 2.218105 \\ A &= 7763.37 \end{aligned} $$STEP 2: To find interest we use formula $ A = P + I $, since $ A = \$7763.37 $ and $ P = \$3500 $ we have:
$$ \begin{aligned} A &= P + I \\ 7763.37 &= 3500 + I \\ I &= 7763.37 - 3500 \\ I &= 4263.37 \end{aligned}$$Please tell me how can I make this better.