Usually, compound interest is calculated at intervals of yearly(annually), half-yearly(semi-annually), quarterly, monthly, etc. Compound interest is the same as reinvesting the interest amount from the investment that makes the money grow very fast over time. All the financial organizations or banks calculate the amount of money based on compound interest. Check the 10th Grade Math articles to know the compound interest when Interest is compounded yearly along with formulae, definition, derivations, etc.

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## Compound Interest Yearly – Definition

Interest compounded yearly or annually is defined as the process of calculating and adding the interest amount to the loan or investment once annually or yearly. The effects of compounding can be seen as the interest is paid. The interest compounded monthly will give higher profits as it is calculated on a higher balance each month. For example, if you borrow $1,00,000 at the interest rate of 5% and interest is compounded annually, after a year you owe $5,250 on the principal amount of $1,05,000.

### What is the Formula for Compound Interest if Compounded Annually? | How to Calculate Compound Interest Annually?

Compound Interest is calculated on the interest accumulated and principal amount over the previous period. In the case that interest is compounded annually, the formula used to calculate compound interest is

Compound Interest = Amount – Principal

C.I. = A – P

Amount A = P{(1 + \(\frac { r }{ 100 } \))^{n}}

Here,

P = Principal Amount

R = Rate of Interest

T = Number of years

A = Amount in t years.

There is also another way of solving annual compound interest rates on the fly in your head. The rule of 72 is the quick trick you can use to estimate the time it would take for the account to double the interest rate.

### Rule of 72 in Calculating Compound Interest Annually

The rule of 72 is the simplified formula that calculates the time for an investment to double in value which is based on the return rate. It applies to anything that increases exponentially like inflation or GDP.

For example, you have a retirement account with a balanced amount of $50,000. The estimation of interest rate is 9% on your investment per year. Now, with the rule of 72, we can just divide the number 72 by the annual interest rate to find out the time it takes to double your balance i.e., 72/9 which is equal to 8. Therefore, your balance will reach 1,00,000 in eight years.

### Compound Interest Compounded Annually Examples

Here we have given different problems with tricks and steps. Solve all the problems and get a grip on the concept.

**Example 1:**

The count of chocolates made in a factory was found to increase at the rate of 2% per hour. Find the chocolates at the end of 2 hours if the initial count was 5,00,000?

**Solution:**

Given that the chocolates count increases at the rate of 2% per hour.

We use the formula, Amount A = P{(1 + \(\frac { r }{ 100 } \))^{n}}

Hence, the choclates at the end of 2 hours = 5,00,000(1 + 2/100)^{2}

= 5,00,000(1 + 0.02)^{2}

= 5,00,000(1.02)^{2}

= 5,20,200

Therefore, the number of chocolates after 2 hours is 5,20,200.

**Example 2:**

The sum of Rs. 20,000 is borrowed by Aakash for 2 years at the interest rate of 10% compounded annually. Find the compound interest and amount to pay at the end of 2 years?

**Solution:**

Given that, Principal amount = Rs. 20,000, Rate = 10% and Time = 2 years.

We can calculate the amount by using the formula, A = P{(1 + \(\frac { r }{ 100 } \))^{n}}

Substituing the values in the above equation,

A= 20,000(1 + 10/100)^{2}

A = 20,000(11/10)(11/10)

A = 24,200

Therefore, the amount to pay at the end of 2 years = Rs. 24,200

Compound Interest for 2nd year = A – P

= 24,200 – 20,000

= 4,200

Therefore, the compound interest = 4,200.

**Example 3:**

What is the compound interest on Rs.3000 for 3 years at 10% per annum compounded annually?

**Solution:**

Given that, Principal amount = Rs. 3000, Time (T) = 3 years, Rate(R) = 10%

We use the formula, A = P{(1 + \(\frac { r }{ 100 } \))^{n}}

A = 3000(1 + 10/100)^{3}

A = 3000(1 + 0.1)^{3}

A = 3000(1.1)^{3}

A = 3990

Interest for the second year = A – P

= 3990 – 3000

= 990

Therefore, the answer is 990.

See More: Practice Test on Compound Interest

### FAQs on Compound Interest Annually

**1. Are compounded annually and compound interest the same?**

Compound interest can be calculated by multiplying the principal amount by 1 plus the raised annual interest rate to the compound period’s number minus 1. Compounded annually refers to the given frequency schedule which varies from continuous to daily to annually.

**2. What will be the formula for compound interest is compounded annually?**

If the principal amount is compounded annually, the final amount after the given time period at the rate of interest percent is A = P(1 + R/100)^{t} and Compound Interest will be A = P(1 + R/100)^{t }– P.

**3. Who benefits from compound interest?**

Mostly the investors get benefit from the compound interest as it is the reinvesting of the amount which helps in growing the money fast over time.

**4. What is Rule 72 and why do they call it Rule 72?**

The actual years are calculated from a logarithmic calculation which is not possible without the help of a calculator with logarithmic capabilities. Hence, the rule of 72 exists. It helps in letting know the time period it takes to double without the help of a physical calculator.

### Summary

Finding Compound interest when Interest is compounded yearly becomes easy if you read this article. Every part of this article is given with an explanation. So, don’t miss the chance to learn the compound interest. Quickly read and get knowledge on the compound interest concept.