Question

How much time will Rs.52000 take to amount to Rs.66625 at 6.25% per annum?

Answer 1

Hint:
To find the time taken, we need to derive a formula as to how the principal \[Rs.\text{ }52000\] will amount to \[Rs.\text{ }66625\] at \[6.25\%\] per annum. For this the formula used to find the time (in years) required is given as:
\[\dfrac{100(A-P)}{PR}=T\]
where \[A\] is the amount reached, \[P\] is the principal, \[R\] is the rate percent per annum and \[T\] is the time taken to reach the amount (in years).

Complete step by step answer:
To find the time(in years) taken to reach the amount of \[Rs.\text{ }66625\] from principal of \[Rs.\text{ }52000\] at $6.25 \% $ per annum is:
\[\dfrac{100(A-P)}{PR}=T\]
Placing the values in the formula as \[A=Rs.\text{ }66625,\text{ }P=Rs.52000,\text{ }R=6.25\%\] we get:
\[\Rightarrow T=\dfrac{100(66625-52000)}{52000\times 6.25}\]
\[\Rightarrow T=\dfrac{100\times 14625}{52000\times 6.25}\]
\[\Rightarrow T=4.5\text{ }years\]

Hence, the time required to reach the amount of \[Rs.\text{ }66625\] from \[Rs.\text{ }52000\] at \[6.25\%\] per annum is \[4.5\text{ }years\].

Note:
Another method to solve for the time required to reach the amount is by subtracting the amount \[Rs.\text{ }66625\] from principal \[Rs.\text{ }52000\], so as to obtain the simple interest of \[Rs.\text{ }66625-Rs.52000=Rs.14625\]. Once the simple interest is obtained we use the formula of \[T=\dfrac{S.I.\times 100}{P\times R}\] to find the time required.