Question

Raghu borrowed rupees \[25000\] at \[20\%\] p.a. compounded half yearly. What amount of money will clear debt after \[1\dfrac{1}{2}\] years?
1). \[Rs.28275\]
2). \[Rs.36275\]
3). \[Rs.33275\]
4). \[Rs.38275\]

Answer 1

Hint: In this question so far, we've been provided principal, a half-yearly compounded rate of interest, and time. As a result, we will calculate the time and rate of interest which is compounded half yearly and apply the amount formula to check which option is correct in the given options.

Complete step-by-step solution:
The main distinction between simple and compound interest is that simple interest is calculated on the principal amount, whereas compound interest is calculated on the principal amount plus the interest compounded for a period cycle.
Simple interest and compound interest are two essential concepts that are commonly employed in various financial services, particularly in banking. Simple interest is used in loans such as instalment loans, auto loans, student loans, and mortgages. Compound interest is employed by the majority of savings accounts to pay interest. It pays a lot more than just interest. Let's take a closer look at the difference between simple and compound interest in this post.
Compound interest is interest earned on both the principal and the interest over a set period of time. The principal is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the next time period. Compound interest is a novel method of calculating interest that is utilised in all financial and economic operations worldwide. When we look at the compound interest values accumulated over successive time periods, we can see how powerful compounding is.
Now according to the question:
We have given that principal amount is \[Rs.25000\]
Rate per interest that is \[r=20\%\] per annum compounded half yearly
Hence rate per interest will be:
 \[\Rightarrow r=\dfrac{20}{2}\]
We have given that amount is compounded half yearly hence time will be \[3\] years.
As we know that to calculate amount we need to apply the formula:
\[\Rightarrow A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]
Substituting the values we get:
\[\Rightarrow A=25000{{\left( 1+\dfrac{20}{2\times 100} \right)}^{3}}\]
\[\Rightarrow A=25000{{\left( 1+0.1 \right)}^{3}}\]
\[\Rightarrow A=25000{{\left( 1.1 \right)}^{3}}\]
\[\Rightarrow A=25000\times 1.331\]
\[\Rightarrow A=33275\]
Hence option \[(3)\] is correct as the amount is \[A=Rs.33275\].

Note: Simple interest is a fixed proportion of the principal amount borrowed or lent that is paid or received over a period of time. In the case of compound interest, interest is always higher than in the case of simple interest and the rate of formula is always given in fraction.