Compound interest is calculated on both the initial payment and the interest earned in previous periods.
problem
If you deposit $4500 into an account paying 7% annual interest compounded semi anualy. Find the amount and interest after 9 years?
solution
The amount is $8358.7 and the interest is $3858.7.
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
$$ P = \$4500 ~,~ r = 7 \% ~ , ~ n = 2 ~ \text{and} ~ t = 9 ~ \text{years}$$After plugging the given information we have
$$ \begin{aligned} A &= 4500 \left( 1 + \frac{ 0.07 }{ 2 } \right)^{\Large{ 2 \cdot 9 }} \\ A &= 4500 \cdot { 1.035 } ^ { 18 } \\ A &= 4500 \cdot 1.857489 \\ A &= 8358.7 \end{aligned} $$STEP 2: To find interest we use formula $ A = P + I $, since $ A = \$8358.7 $ and $ P = \$4500 $ we have:
$$ \begin{aligned} A &= P + I \\ 8358.7 &= 4500 + I \\ I &= 8358.7 - 4500 \\ I &= 3858.7 \end{aligned}$$