Question

A man borrows Rs. $18,000$ at $5$% per annum compound interest. If he repays Rs. $6,000$ at the end of the first year and Rs. $8,000$ at the end of the second year; how much he should pay at the end of the third year in order to clear the account? Answer correctly to the nearest rupee.

Answer 1

For the first year
$P=Rs18,000$
$N=1year$
$R=5$ %
We have $S.I.=\frac{PNR}{100}=\frac{18,000\times 1\times 5}{100}=Rs900$
And Amount at the end of first year $P+S.I.=Rs18,000+Rs900=Rs18,900$
Now, for the second year
$P=Rs18,900-Rs6,000=Rs12,900$
$N=1year$
$R=5$ %
We have $S.I.=\frac{PNR}{100}=\frac{12,900\times 1\times 5}{100}=Rs645$
And Amount at the end of second year $P+S.I.=Rs12,900+Rs645=Rs13,545$
Also, for the third year
$P=Rs13,545-Rs8,000=Rs5,545$
$N=1year$
$R=5$ %
We have $S.I.=\frac{PNR}{100}=\frac{5,545\times 1\times 5}{100}=Rs277.25$
And Amount at the end of third year $P+S.I.=Rs5,545+Rs277.25=Rs5,822.25$
Thus, at the end of the third year, amount to be paid $=Rs5,822.25$ or approximately $Rs5,822$