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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. Click here to view some problem which can be solved by using this calculator. Problem If you deposit$4500 into an account paying 7% annual interest compounded semi anualy , how much money will be in the account after 9 years?

Result

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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Imputed values: 0 , 4500 , 7 , 9 , 1 , 2

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## Compound Interest Problems

This is a list of the example problems which can be solved by using this calculator.

### Problems with unknown interest and amount

Example 1: What will a deposit of \$4,500 at 7% compounded yearly interest be worth if left in the bank for 9 years?  Set up the form View the solution Example 2: What will a deposit of$3,500 at 10% compounded monthly be worth if left in the bank for 8 years?

 Set up the form View the solution

### Problems with unknown principal

Example 3: How much money would you need to deposit today at 8% annual interest compounded monthly to have \$1200 in the account after 12 years?  Set up the form View the solution Example 4: Find the present value of \$1,000 to be received at the end of 2 years at a 12% nominal annual interest rate compounded quarterly.

 Set up the form View the solution

### Problems with unknown interest rate

Example 5: What annual interest rate is implied if you lend someone $1,700 and are repaid$1,910 in two years?

 Set up the form View the solution

Example 6: Suppose that a savings account is compounded monthly with a principal of \$1350. After 8 months, the amount increased to \$1424. What was the per annum interest rate?

 Set up the form View the solution

### Example with unknown time period

Example 7: How long does it take for \$4,300 to grow into \$2,720 at 9% compounded quarterly?

 Set up the form View the solution

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