| A builder borrows Rs. 2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 yr in two equal yearly instalments. |
| How much will each instalment be? |
A) Rs. 1352
B) Rs. 1377
C) Rs. 1275
D) Rs. 1283
Correct Answer: A
Solution :
A = Rs. 2550 R = 4% per annum and n = 2 yr Let each of the equal instalment be Rs. X. Present worth\[=\frac{\text{Instalment}}{{{\left( 1+\frac{r}{100} \right)}^{n}}}\] \[\Rightarrow \,\] \[{{P}_{1}}=\frac{x}{{{\left( 1+\frac{4}{100} \right)}^{1}}}=\frac{x}{1+\frac{1}{25}}=\frac{x}{\frac{26}{25}}\] \[\therefore \,\,\] \[{{P}_{1}}=\frac{25}{26}x\] Similarly, \[{{p}_{2}}={{\left( \frac{25}{26} \right)}^{2}}x=\frac{625}{676}x\] \[\therefore \,\,\] \[{{P}_{1}}+{{P}_{2}}=A\] \[\Rightarrow \,\] \[\frac{25}{26}x+\frac{625}{676}x=2550\] \[\Rightarrow \,\] \[\frac{(650+625)x}{676}=2550\] \[\Rightarrow \,\] \[\,\frac{1275}{676}x=2550\] \[\Rightarrow \,\]\[x=2550\times \frac{676}{1275}\] \[\therefore \]x = Rs. 1352
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