| A man borrows Rs. 5000 from a bank at 8% per annum compound interest. At the end of every year he pays Rs. 1000 as a part payment of loan and interest. How much does he still owe to the bank after 3 such instalments? |
A) Rs. 3052.16
B) Rs. 3442.20
C) Rs. 3616.84
D) Rs. 3824.40
Correct Answer: A
Solution :
| Borrows amount = Rs. 5000 |
| Rate of interest \[=8\]% |
| Number of instalments \[=3\] |
| According to the question, |
| Balance \[=\text{Rs}\text{. }\left\{ 5000\times {{\left( 1+\frac{8}{100} \right)}^{3}} \right\}\] |
| \[-\left\{ 1000\times {{\left( 1+\frac{8}{100} \right)}^{2}}+1000\times \left( 1+\frac{8}{100} \right)+1000 \right\}\] \[=\left[ \left( 5000\times \frac{27}{25}\times \frac{27}{25}\times \frac{27}{25} \right) \right]\] |
| \[-\left( 1000\times \frac{27}{25}\times \frac{27}{25}+1000\times \frac{27}{25}+1000 \right)\] |
| \[=\left[ \frac{157464}{25}-\left( \frac{5832}{5}+1080+1000 \right) \right]\] |
| \[=\left( \frac{157464}{25}-\frac{16232}{5} \right)\] |
| \[=6298.56-3246.40=3052.16\] |
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