Compound Interest is calculated on the initial payment and also on the interest of previous periods.
Example: Suppose you give \$100 to a bank which pays you 10% compound interest at the end of every year. After one year you will have \$100 + 10% = \$110, and after two years you will have \$110 + 10% = \$121.
Problem:
How much money would you need to deposit today at 8% annual interest compounded monthly to have $1200 in the account after 12 years?
Result:
The principal is $460.72.
Explanation:
To find amount we use formula:
$$ A = P \left( 1 + \frac{r}{n} \right)^{\Large{n \cdot t}} $$ |
A = total amount P = principal or amount of money deposited, r = annual interest rate n = number of times compounded per year t = time in years |
In this example we have
$$ A = \$1200 ~,~ r = 8 \% ~ , ~ n = 12 ~ \text{and} ~ t = 12 ~ \text{years}$$After plugging the given information we have
$$ \begin{aligned} 1200 &= P \left( 1 + \frac{ 0.08 }{ 12 } \right)^{\Large{ 12 \cdot 12 }} \\ 1200 &= P \cdot { 1.00667 } ^ { 144 } \\ 1200 &= P \cdot 2.604631 \\ P &= \frac{ 1200 }{ 2.604631} \\ P &= 460.72 \end{aligned}$$Share this result with others by using the link below.
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