A man borrows $Rs.5,000$ at $12$ percent compound interest payable every six months. He repays $Rs.1,800$ at the end of every six months. Calculate the third payment he has to make at the end of $18$ months in order to clear the entire loan.
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Answer
For $1^{\text {st }}$ six months :
$P= Rs. 5,000, R=12\ \%\ $ and $T=6$ months $=\frac{1}{2}$ year
$\therefore$ Interest $=\frac{5,000 \times 12 \times 1}{2 \times 100}= Rs. 300 .$
And, Amount $= Rs. 5,000+ Rs.300= Rs. 5,300$
Since, money repaid $= Rs. 1,800$
Balance $= Rs. 5,300- Rs. 1,800= Rs. 3,500$
For $2^{\text {nd }}$ six months :
$P= Rs. 3,500, R=12\ \%\ $ and $T=6$ months $=\frac{1}{2}$ year
$\therefore$ Interest $=\frac{3,500 \times 12 \times 1}{2 \times 100}=\text { Rs. } 210 \text {. }$
And, Amount $= Rs. 3,500+ Rs. 210= Rs. 3,710 .$
Again money repaid $= Rs. 1,800$
Balance $= Rs. 3,710- Rs. 1,800= Rs. 1,910 .$
For $3^{\text {rd }}$ six months :
$P= Rs. 1,910, R=12\ \%\ $ and $T=6$ months $=\frac{1}{2}$ year
$\therefore$ Interest $=\frac{1,910 \times 12 \times 1}{2 \times 100}= Rs. 114.60 .$
And, Amount $= Rs. 1,910+ Rs. 114.60= Rs. 2,024.60$
Thus, the $3^{\text {rd }}$ payment to be made to clear the entire loan is $2,024.60$.
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