Calculate the amount and the compound interest on $R s 5000$ in $2$ years when the rate for interest for successive years is $6 %$ and $8 %$ respectively.

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Solution

$1^{s t} y e a r$
Principal, $P = R s .5000$
Time, $T = 1 y e a r$
Rate of interest , $R = 6 %$
$∴$ simple Interest, $S I = \frac{P T R}{100} = \frac{5000 \times 10 \times 6}{100} = R s .300$
$∴ A m o u n t = P + S I = R s .5300$
$2 n d y e a r$
Principal = Amount of $1 s t y e a r = R s .5300$
Rate of interest $= 8 %$
Time $= 1 y e a r$
$∴$ Interest $= \frac{5300 \times 1 \times 8}{100} = R s .424$
$∴$ Amount $= R s . (5300 + 424) = R s .5724$
The interest of $2 n d$ year is the required compound interest. So, $C . I = r s .424$ and the required amount is $R s .5724$

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