Calculate the compound interest on Rs 16000 for 2 years 10% per annum when compounded half yearly

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The power of compounding grows your savings faster

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• Save more with compound interest
• Compound interest formula
• How to calculate compound interest

3 minutes

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

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 balanceP = 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)24A = $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.

Find the amount and the compound interest on Rs 160000 for 2 years at 10% per annum, compounded half yearly.

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Find the amount and compound interest for Rs.16000 for 2 year at 10% per annum compounded half-yearly.

Answer

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Hint: Here we go through by putting the formula of amount as we read in chapter compound interest because we have to find the amount and for the compound interest we subtract principal amount from the amount we find at the end of two years compounded half-yearly.

Complete step-by-step answer:
Here in the question it is given that a principal amount is Rs.16000 i.e. the given principal Amount (P) =RS.16000
The given time period (T) =2 years.
And the given rate(R) =10% compounded half-yearly.
Here the interest is compounded half yearly so n=2
Let us apply the formula of amount i.e. $A = P{\left( {1 + \dfrac{R}{n}} \right)^{nt}}$
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount) =Rs16000
r = the annual interest rate=10%
n = the number of times that interest is compounded per unit =2
t = the time the money is invested or borrowed for=2
Now put these value in formula we get,
$
   \Rightarrow A = 16000{\left( {1 + \dfrac{{10\% }}{2}} \right)^{2 \times 2}} \\
   \Rightarrow A = 16000{\left( {1 + \dfrac{{10}}{{2 \times 100}}} \right)^4} \\
   \Rightarrow A = 16000{\left( {\dfrac{{21}}{{20}}} \right)^4} \\
   \Rightarrow A = \dfrac{{16000 \times 21 \times 21 \times 21 \times 21}}{{20 \times 20 \times 20 \times 20}} \\
   \Rightarrow A = \dfrac{{{\text{194481}}}}{{10}} \\
  \therefore A = 19448.1 \\
 $
Therefore, compound interest= amount – principal amount=19448.1-16000=3448.1
Hence Amount=Rs.19448.1 and compound interest=Rs.3448.1

Note: Whenever we face such a type of question the key concept for solving the question is just simply put the formula in which the given terms of question are used and find out the unknown term that question asked by the help of that formula. Here in this question the principal amount, time and rate are given and we have to find the amount so we apply the formula of amount.

How much would a sum of 16000 amount to in 2 years at 10% per annum if the interest is compounded half yearly?

What is the interest earned on Rs 1000 for 2 years at 10% per annum compound interest compounded annually?

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How do you calculate interest compounded half yearly?