Question

Simple interest on a certain sum of mine at \[9\% \] is rupees \[450\] in \[2\] years. Find the compound interest on the same sum at the same rate for \[1\] year if the interest is reckoned half-yearly.

Answer 1

Hint: The simple interest is a type of interest that is applied to the amount borrowed or invested for the entire duration of the loan, without taking any other factors into account, such as past interest or any other financial considerations and compound interest is the interest which is calculated on the principal and the interest that is accumulated over the previous tenure. Thus, the compound interest is also called interest on interest.

Complete step by step answer:
 Let us write the given data:
Simple interest for \[1\] year \[ = \dfrac{{450}}{2}\]
\[ = 225\]
Let \[x\] be the principal,
\[ \Rightarrow \dfrac{{9x}}{{100}} = 225\]
\[x = 2500\]
With respect to sum at \[9\% \], we have:
\[ \Rightarrow 2500 \times \left( {\dfrac{9}{{100}}} \right) = 225\]
Hence, capital for second half year is
\[ = 2725\]
With respect to sum at \[9\% \], we have:
\[ \Rightarrow 2725 \times \left( {\dfrac{9}{{100}}} \right) = 245.25\]
Hence, the compound interest for one year is
\[ = 225 + 245.25\]
\[ = 470.25\]
Therefore, compound interest on the same sum at the same rate is \[470.25\] , only when the interest is not per annum.

Note: Simple interest is generally applied to short-term loans, usually one year or less, that are administered by financial companies. The same applies to money invested for a similarly short period of time. The simple interest rate is a ratio and is typically expressed as a percentage.