A sum of Rs. 10,000 is borrowed at 8% per annum compounded annually. If the amount is to be paid in three equal installments,what will be the annual installment?

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Solution

Let the each installment be x
$10, 000 = \frac{x}{1 + \frac{8}{100}} + \frac{x}{(1 + \frac{8}{100})^{2}} + \frac{x}{(1 + \frac{8}{100})^{3}}$
$10, 000 = \frac{100 x}{108} + \frac{100^{2} x}{(108)^{2}} + (\frac{100}{108})^{3} x$
$10, 000 = \frac{25}{27} x + (\frac{25}{27})^{2} x + (\frac{25}{27})^{3} x$
$= \frac{25 x}{27} (1 + \frac{25}{27} + (\frac{25}{27})^{2})$
$\Rightarrow 10, 000 = \frac{25 x}{27} (\frac{2029}{729})$
$∴ x = 3880.335$ on simplifying

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A sum of Rs. 10,000 is borrowed at 8% per annum compounded annually. If the amount is to be paid in three equal installments,what will be the annual installment?

Let the each installment be x10,000=x1+8100+x(1+8100)2+x(1+8100)310,000=100x108+1002x(108)2+(100108)3x10,000=2527x+(2527)2x+(2527)3x=25x27(1+2527+(2527)2)⇒10,000=25x27(2029729)∴x=3880.335 on simplifying