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51.
There is 100% increase to an amount in 8 yr, at simple interest. Find the compound interest of ₹ 8000 after 2 yr at the same rate of interest.

₹ 2500

₹ 2000

₹ 2250

₹ 2125

₹ 2125

Let the rate of interest be r and principal be x.
After 8 yr, principal becomes 2x, i.e. Amount = ₹ 2x
∴ Interest = 2x - x = ₹ x
$straight P space equals space fraction numerator straight x space cross times space straight r space cross times space 8 over denominator 100 end fraction straight x space equals space fraction numerator straight x space cross times space straight r space cross times space 8 over denominator 100 end fraction 2 straight r space equals space 25 comma space space space straight r space equals space 25 over 2 space equals space 12 1 half percent sign$

Case II,
P = ₹ 8000, r = 12.5% n = 2 yrs

$straight A space equals space straight P open parentheses 1 space plus space straight r over 100 close parentheses to the power of straight n straight A space equals space 8000 open parentheses 1 space plus space fraction numerator 25 over denominator 2 space cross times space 100 end fraction close parentheses squared straight A space equals space 8000 open parentheses 9 over 8 close parentheses squared space space space space equals space fraction numerator 8000 space cross times space 81 over denominator 64 end fraction space equals space ₹ space 10125$
∴ Compound interest = ₹ (10125 - 8000) = ₹ 2125.

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52.

The compound interest earned in two years at 12% per annum is ₹ 10,176/-. What is the sum (in ₹) invested?

₹ 50,000/-
₹ 60,000/-
₹ 40,000/-
₹ 80,000/-

53.

The simple and compound interest that can be earned in two years at the same rate is ₹ 4,000/- and ₹ 4,180/- respectively. What is the rate(% per annum) of interest?