IMPORTANT FORMULAE :-
Let, Principal = p
Time = n years
Rate = r % per annum
CASE 1 :- When compound interest is annually.
Amount = $p \left ( 1+\frac{r}{100} \right )^{n}$
CASE 2 :- When compound interest is half yearly.
Amount = $p \left ( 1+\frac{\frac{r}{2}}{100} \right )^{2n}$
CASE 3 :- When compound interest is quarterly.
Amount = $p \left ( 1+\frac{\frac{r}{4}}{100} \right )^{4n}$
CASE 4 :- When rate of interest is $r_{1}\, \%,\, r_{2}\, \%\, and\, r_{3}\, \%$ for 1st year, 2nd year and 3rd year respectively,
Then,
Amount = $p\left ( 1+\frac{r_{1}}{100} \right )\times \left ( 1+\frac{r_{2}}{100} \right )\times \left ( 1+\frac{r_{3}}{100} \right )$
Example 1:- Find the compound interest on Rs 10000 in 2 years at 4 % per annum, the interest being compounded half-yearly?
Sol.
Principal = Rs 10000
Rate = 2 % per half-yearly
Time = 2 years = 4 half-years
$\therefore$ Amount = $10000\times \left ( 1+\frac{2}{100} \right )^{4}$
= $\left ( 10000\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50} \right )$
= Rs 10824.32
$\therefore$ C.I. = Rs (10824.32 - 10000)
= Rs 824.32
Example 2 :- Find compound interest on Rs 8000 at 15 % per annum for 2 years 8 months, compounded annually?
Sol.
Principal = Rs 8000
Rate = 15 %
Time = 2 years 8 months = $2\frac{8}{12}$ years = $2\frac{2}{3}$
Amount = $8000\times \left ( 1+\frac{15}{100} \right )^{2}\times \left ( 1+\frac{\frac{2}{3}\times 15}{100} \right )$
= $\left ( 8000\times \frac{23}{20}\times \frac{23}{20}\times \frac{11}{10} \right )$
= Rs 11638
$\therefore$ C.I. = Rs (11638 - 8000)
= Rs 3638
Let, Principal = p
Time = n years
Rate = r % per annum
CASE 1 :- When compound interest is annually.
Amount = $p \left ( 1+\frac{r}{100} \right )^{n}$
CASE 2 :- When compound interest is half yearly.
Amount = $p \left ( 1+\frac{\frac{r}{2}}{100} \right )^{2n}$
CASE 3 :- When compound interest is quarterly.
Amount = $p \left ( 1+\frac{\frac{r}{4}}{100} \right )^{4n}$
CASE 4 :- When rate of interest is $r_{1}\, \%,\, r_{2}\, \%\, and\, r_{3}\, \%$ for 1st year, 2nd year and 3rd year respectively,
Then,
Amount = $p\left ( 1+\frac{r_{1}}{100} \right )\times \left ( 1+\frac{r_{2}}{100} \right )\times \left ( 1+\frac{r_{3}}{100} \right )$
Example 1:- Find the compound interest on Rs 10000 in 2 years at 4 % per annum, the interest being compounded half-yearly?
Sol.
Principal = Rs 10000
Rate = 2 % per half-yearly
Time = 2 years = 4 half-years
$\therefore$ Amount = $10000\times \left ( 1+\frac{2}{100} \right )^{4}$
= $\left ( 10000\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50}\times \frac{51}{50} \right )$
= Rs 10824.32
$\therefore$ C.I. = Rs (10824.32 - 10000)
= Rs 824.32
Example 2 :- Find compound interest on Rs 8000 at 15 % per annum for 2 years 8 months, compounded annually?
Sol.
Principal = Rs 8000
Rate = 15 %
Time = 2 years 8 months = $2\frac{8}{12}$ years = $2\frac{2}{3}$
Amount = $8000\times \left ( 1+\frac{15}{100} \right )^{2}\times \left ( 1+\frac{\frac{2}{3}\times 15}{100} \right )$
= $\left ( 8000\times \frac{23}{20}\times \frac{23}{20}\times \frac{11}{10} \right )$
= Rs 11638
$\therefore$ C.I. = Rs (11638 - 8000)
= Rs 3638
No comments:
Post a Comment