Compound interest is calculated on both the initial payment and the interest earned in previous periods.
problem
How much money would you need to deposit today at 12% annual interest compounded quarterly to have $1000 in the account after 2 years?
solution
The principal is $789.41.
explanation
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
$$ A = \$1000 ~,~ r = 12 \% ~ , ~ n = 4 ~ \text{and} ~ t = 2 ~ \text{years} $$After plugging the given information we have
$$ \begin{aligned} 1000 &= P \left( 1 + \frac{ 0.12 }{ 4 } \right)^{\Large{ 4 \cdot 2 }} \\ 1000 &= P \cdot { 1.03 } ^ { 8 } \\ 1000 &= P \cdot 1.26677 \\ P &= \frac{ 1000 }{ 1.26677} \\ P &= 789.41 \end{aligned} $$Please tell me how can I make this better.