Question

the rate of simple interest per annum of bank being increased from 10.5 percent to 18 percent and time duration is also increased from 4.5 years to 7 years. The total simple interest was increased by Rs 1250. find the increased simple interest. ​

Answer 1

The increased simple interest on the same principal is Rs 2000.

Let us consider the principal amount that was placed in the bank as Rs x.

Initial rate = 10.5% per annum or, r = 0.105

Initial time(t) = 4.5 years

interest earned is calculated by using the formula: $I=p\times r\times t$

Interest earned :

$1 = x\times 0.105\times 4.5 = 0.4725x$

Now the new rate of interest is 18%

Hence $r_2=0.18$ and time is increased to 7 years, hence $t_2=7$

Now we will use the same above formula to calculate the extended interest on the same principal "x" .

New interest :

$I_2 = p\times r_2 \times t_2\\or, I_2 = x\times 0.18\times 7\\or, I_2 = 1.26x$

Now it is given that the new interest is Rs 1250 more, hence we form a linear equation in x :

$1.26x-0.4725x = 1250\\or, 0.7875 x = 1250\\or, x = 1250\div 0.7875\\or,x\approx =1587.30$

Increased simple interest $= 1.26x = 1.26\times 1587.30 = 2000$

Therefore the increased simple interest is Rs 2000.

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