Question

Shilpa borrowed rupees ₹40960 from State Bank of India at 12 1/2% per annum compounded annually. On the same day she lent out his money to Sunita at the same rate of interest but compounded semi-annually. Find her gain after 1 1/2 years

Answer 1

There is no gain

Step-by-step explanation:

Given that,

Principal = Rs. 40,960

Rate = 12 $\frac{1}{2}$%

Time = 1 $\frac{1}{2}$years = 18/12 or 3/2

Using the formula, A = P(1 + $\frac{r}{n})^{nt}$

= 40960(1 + $\frac{12.5}{200}) ^{2*\frac{3}{2} }$

= 40,960( 1 + 125/2000)"3

= Rs. 49130

C.I. = A - P

= Rs. 49130 - Rs. 40960

= Rs. 8170

For compounded semi-annually,

n = 3

r = 12.5/2% or 6.25%

so,

A = P(1 + $\frac{r}{n})^{nt}$

= 40,960$(1 + 6.25/100)^{3}$

= 40,960$(1.0625)^{3}$

= Rs. 49130

Thus, the amount Shipa receives and pays is the same.

Learn more: Compound interest

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