Pankaj takes a loan of Rs. 10000 at $10 %$ per annum compounded annually which is to be repaid in two equal annual installments: one at the end of the first year and second at the end of the second year. The value of each installment is:

Rs. 5760

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Rs. 5500

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Rs. 5650

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Rs. 5800

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Solution

The correct option is A Rs. 5760
$10, 000 (1.1)^{2} = x [1 + (1.1)]$
x = 5761.9

Alternatively:
Let the value of each installment is X, Total amount is P
$P = X (K + K^{2} + K^{3} + . . . . . . . . . . . . . . . . . . .),$
$W h e r e K = \frac{100}{100 + r}$
Here only two years and r is $10 %$ then
$P = X (K + K^{2})$
$10000 = x {\frac{10}{11} + {(\frac{10}{11})}^{2}}$
X = 5761.9

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Pankaj takes a loan of Rs. 10000 at 10% per annum compounded annually which is to be repaid in two equal annual installments: one at the end of the first year and second at the end of the second year. The value of each installment is:

The correct option is A Rs. 576010,000(1.1)2=x[1+(1.1)] x = 5761.9 Alternatively: Let the value of each installment is X, Total amount is P P=X(K+K2+K3+...................), Where K=100100+r Here only two years and r is 10% then P=X(K+K2) 10000=x{1011+(1011)2} X = 5761.9

Pankaj takes a loan of Rs. 10000 at $10 %$ per annum compounded annually which is to be repaid in two equal annual installments: one at the end of the first year and second at the end of the second year. The value of each installment is: