Calculate the compound interest on Rs 10000 at 5 pa for 2 years

The sooner you start to save, the more you'll earn with compound interest.

How compound interest works

Compound interest is the interest you get on:

• the money you initially deposited, called the principal
• the interest you've already earned

For example, if you have a savings account, you'll earn interest on your initial savings and on the interest you've already earned. You get interest on your interest.

This is different to simple interest. Simple interest is paid only on the principal at the end of the period. A term deposit usually earns simple interest.

Save more with compound interest

The power of compounding helps you to save more money. The longer you save, the more interest you earn. So start as soon as you can and save regularly. You'll earn a lot more than if you try to catch up later.

For example, if you put $10,000 into a savings account with 3% interest compounded monthly:

• After five years, you'd have $11,616. You'd earn $1,616 in interest.
• After 10 years you'd have $13,494. You'd earn $3,494 in interest.
• After 20 years you'd have $18,208. You'd earn $8,208 in interest.

Compound interest formula

To calculate compound interest, use the formula:

A = P x (1 + r)n

A = ending balance
P = starting balance (or principal)
r = interest rate per period as a decimal (for example, 2% becomes 0.02)
n = the number of time periods

How to calculate compound interest

To calculate how much $2,000 will earn over two years at an interest rate of 5% per year, compounded monthly:

1. Divide the annual interest rate of 5% by 12 (as interest compounds monthly) = 0.0042

2. Calculate the number of time periods (n) in months you'll be earning interest for (2 years x 12 months per year) = 24

3. Use the compound interest formula

A = $2,000 x (1+ 0.0042)24
A = $2,000 x 1.106
A = $2,211.64

Lorenzo and Sophia compare the compounding effect

Lorenzo and Sophia both decide to invest $10,000 at a 5% interest rate for five years. Sophia earns interest monthly, and Lorenzo earns interest at the end of the five-year term.

After five years:

• Sophia has $12,834.
• Lorenzo has $12,500.

Sophia and Lorenzo both started with the same amount. But Sophia gets $334 more interest than Lorenzo because of the compounding effect. Because Sophia is paid interest each month, the following month she earns interest on interest.

Answer

Verified

Hint: First we recall the definition and formula of compound interest and then calculate the compound interest. The formula used to calculate the compound interest is
Compound interest = Amount – Principal
And \[\text{Amount =}P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
Where, $P=$ Principal
\[R=\] Rate of interest
$T=$Time period

Complete step by step answer:
Now, we have given that Principal sum $=10,000$
Rate of interest $=4%$ per annum
Time period \[=2\text{ years}\]
We have given that the compound interest being compounded half yearly, so the time period will be $4\text{ years}$and the rate of interest will be half i.e. $2%$ because when interest is compounded half yearly the rate of interest will be $\dfrac{R}{2}$.
Now, we have to calculate the Amount, so we put all values in the formula
\[\text{Amount =}P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
$\Rightarrow 10000{{\left( 1+\dfrac{2}{100} \right)}^{4}}$
$\begin{align}
  & \Rightarrow 10000{{\left( 1+\dfrac{1}{50} \right)}^{4}} \\
 & \Rightarrow 10000\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right)\times \left( \dfrac{51}{50} \right) \\
 & \Rightarrow 10.2\times 10.2\times 10.2\times 10.2 \\
 & \Rightarrow 10824.32 \\
\end{align}$
The Amount will be Rs. $10824.32$
Now we have to calculate compound interest.
We know that Compound interest = Amount – Principal
Putting the values, Compound interest will be
 $\begin{align}
  & =10824.32-10000 \\
 & =824.32 \\
\end{align}$
So, the compound interest on Rs $10000$ in $2$ years at $4%$ per annum being compounded half yearly is $Rs.824.32$.

So, the correct answer is “Option C”.

Note: Compound interest is interest on interest; it means compound interest is additional amount of interest to the principal sum. Before calculating compound interest students have to calculate the amount by using the formula and then subtract principal from amount. Students must read questions carefully about the compounding frequency i.e. interest compounded yearly, half-yearly, quarterly, monthly or weekly. The time period will be changed accordingly.

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