If a sum of Rs. 13040 is to be repaid in two equal installments at $$3\frac{3}{4}$$ % per annum, what is the amount of each installment?

$$\eqalign{ & {\text{Let}}\,{\text{each}}\,{\text{installment}}\,{\text{be}}\,P \cr & {\text{Hence}}, \cr & {\frac{x}{{ {\left( {\frac{{100}}{{100 + r}}} \right) + {{\left( {\frac{{100}}{{100 + r}}} \right)}^2}} }}} \cr & Or,\,\frac{x}{{ {1 + {\frac{{15}}{{400}}} } }} + \frac{x}{{ {1 + {{\left( {\frac{{15}}{{400}}} \right)}^2}} }} = Rs.\,13040 \cr & {\text{On}}\,{\text{solving,}}\,{\text{it}}\,{\text{gives}}\,x = Rs.\,6889 \cr} $$