Question

Meera deposits ₹ 30,000 in a bank account that pays a simple interest at the rate of \[7.5\% \] per annum. For how many years should she invest to generate ₹ 45,000?

Answer 1

Hint:
To find the time first we have to find the simple interest
Then by using the formula, S = $\left( {\dfrac{{P \times r \times t}}{{100}}} \right)$, we have to find the value of “t”.

Complete step by step solution:
Here we are given that Meera deposits ₹ 30,000 in a bank account that pays a simple interest at the rate of \[7.5\% \] per annum.
We have to find out how many years should she invest to generate ₹ 45,000?
We have to given that,
P = 30000
R = \[7.5\% \]
Time = t (assume)
A = 45000
Now,
Simple Interest (SI) = P – A
\[ = {\text{ }}45000{\text{ }}-{\text{ }}30000\]
\[ = {\text{ }}15000\]
\[150000 = \left( {30000 \times 7.5 \times t} \right) * 100\]
$1500000 = 30000 \times 7.5 \times t$
Now, make “t” as a subject
$t = \dfrac{{1500000}}{{\left( {30000 \times 7.5} \right)}}$
$t = \dfrac{{50}}{{7.5}} = 6$is to $\dfrac{2}{3}$
$\therefore t = $ 6 YEARS 4 MONTHS

To generate 45,000, she should invest 6years 4months.

Note:
Simple Interest: Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principle by the number of days that elapse between payments.
 Simple Interest (SI) = $\left( {\dfrac{{P \times r \times t}}{{100}}} \right)$where,
P = Principle amount
r = Rate of interest
t = time period
Compound interest: Compound Interest is the addition of interest to the principle sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Compound Interest = $A = P{\left( {1 + \dfrac{r}{n}} \right)^{nt}}$ where,
A = Final amount
P = Initial principal balance
r = Interest rate
n = number of times interest applied per time period
t = number of time periods elapsed