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Compound interest calculator

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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:

$$ \begin{aligned} A &= P + I \\ 8358.7 &= 4500 + I \\ I &= 8358.7 - 4500 \\ I &= 3858.7 \end{aligned}$$

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Examples:
example 1:ex 1:
What is the value of a $4500 deposit at 7% compounded annual interest if it is held in a bank for 9 years?
example 2:ex 2:
What will a $3500 deposit at 10% compounded monthly be worth after 8 years in the bank?
example 3:ex 3:
How much money would you need to put today at 8% annual compounded monthly interest to have $1200 in the account after 12 years?
example 4:ex 4:
Determine the present value of $1000 at a 12% annual interest rate compounded quarterly at the end of two years.
example 5:ex 5:
What is the estimated yearly interest rate if you give someone $1700 and get repaid $1910 in two years?
example 6:ex 6:
Assume that a savings account with a principal of $1350 is compounded monthly. After 8 months, the total had risen to $1424. What was the interest rate per year?
example 7:ex 7:
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