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A sum of Rs. \[800\] amounts to Rs.\[\;920\] in \[3\] years at simple interest. If the rate of interest is increased by \[\;5\% \], then the amount will increase to______

Last updated date: 13th Jun 2024
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Hint:First we find an interest for the given data and then we find rate of interest by using the simple interest formula.Also the given data said that the rate of interest is increased. Repeat the above process, we will get the simple interest for the increased rate of interest and find the total amount.

Formula used:$\text{Simple interest = Total amount – Principle}$.

Complete step-by-step answer:
It is given that the Principal amount is \[800\]
Time taken for \[3\] years, Total amount \[\; = 920\]
Increasing interest rate by \[\;5\% \]
First we find
Simple Interest for \[3\] years = $\text{Total amount – Principle}$.
\[\; = 920 - 800 = 120\]
We know that Simple Interest \[ = \dfrac{{Principle \times Time \times Rate}}{{100}}\]
Interest rate\[ = \dfrac{{{\text{Simple Interest}} \times 100}}{{Principle \times Time}}\]
Interest rate\[ = \dfrac{{{\text{120}} \times 100}}{{800 \times 3}}\]
Interest rate \[\; = 5\% \]
New interest rate\[ = {\text{ }}5{\text{ }} + {\text{ }}5{\text{ }} = {\text{ }}10\% \], Principal \[ = {\text{ }}800\], Time \[ = {\text{ }}3\] years.
Simple Interest\[ = \dfrac{{Principle \times Time \times Rate}}{{100}}\]
Simple Interest\[ = \dfrac{{800 \times 10 \times 3}}{{100}}\]
Simple Interest \[ = Rs{\text{ }}240\].
The new amount = principle + new interest
                          \[ = 800 + 240 = 1040\]

Therefore, if the rate of interest is increased by \[\;5\% \], then the amount will increases to $Rs.1040$.

Note:Simple interest is determined by multiplying the daily interest rate by the principal of the number of days that elapse between payments. By using the simple interest formula get the previous interest rate then add the given rate. Find simple interest with the new rate. Now we subtract both the total amount and we will get an increasing amount.