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# Compound interest calculator

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 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 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

$$P = \4500 ~,~ r = 7 \% ~ , ~ n = 2 ~ \text{and} ~ t = 9 ~ \text{years}$$

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}

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examples
example 1:ex 1:
What will a deposit of $\color{blue}{\$4500}$at$\color{blue}{7\%}$compounded$\color{blue}{\text{yearly}}$interest be worth if left in the bank for$\color{blue}{\text{9 years}}$? example 2:ex 2: What will a deposit of$\color{blue}{\$3500}$ at $\color{blue}{10\,\%}$ compounded $\color{blue}{\text{monthly}}$ be worth if left in the bank for $\color{blue}{8 \, \text{years}}$ ?
example 3:ex 3:
How much money would you need to deposit today at $\color{blue}{8\% \, \text{annual}}$ interest compounded $\color{blue}{\text{monthly}}$ to have $\color{blue}{\$1200}$in the account after$\color{blue}{12 \, \text{years}} \, \text{?}$example 4:ex 4: Find the present value of$\color{blue}{\$1000}$ to be received at the end of $\color{blue}{2 \, \text{years}}$ at a $\color{blue}{12\%}$ nominal annual interest rate compounded $\color{blue}{\text{quarterly}}$.
example 5:ex 5:
What annual interest rate is implied if you lend someone $\color{blue}{\$1700}$and are repaid$\color{blue}{\$1910}$ in $\color{blue}{\text{two years}}$?
example 6:ex 6:
Suppose that a savings account is compounded $\color{blue}{\text{monthly}}$ with a principal of $\color{blue}{\$1350}$. After$\color{blue}{8 \, \text{months}}$, the amount increased to$\color{blue}{\$1424}$. What was the per annum interest rate?
example 7:ex 7:
How long does it take for $\color{blue}{\$4300}$to grow into$\color{blue}{\$6720}$ at $\color{blue}{9\,\%}$ compounded $\color{blue}{\text{quarterly}}$?
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