Principal = Rs.20000, Rate of interest = 18%, Time = 2 years.
When Interest Compounded Annually:
Amount = P $\displaystyle \left( 1 + \frac{\text{R}}{100}\right)^n $
= 22000 $\displaystyle \left( 1 + \frac{18}{100}\right)^2 = \left(\frac{118}{100}\right)^2 $
= 22000 $\displaystyle \left(\frac{59}{50}\right)^2 = 22000 \frac{59}{50} \times \frac{59}{50}$ = 27848.
Amount = Rs.27848
Interest payable = Amount – Principal = Rs.27848 – Rs.20000 = Rs.7848.
[Or] Direct method:
Principal |
= |
20000 |
||
1st year@ 18% |
= |
3600 |
||
23600 |
||||
2nd year@18% |
4248 |
|||
Amount |
= |
27848 |
=> Interest payable = Rs.27848 – Rs.20000 = Rs.7848
P = Rs.18000; R = 10% half yearly; T = 2 years.
When Interest Compounded Half Yearly:
Amount = P $\displaystyle \left( 1 + \frac{\frac{\text{R}}{2}}{100}\right )^{2n} $
=> 18000 $\displaystyle \left( 1 + \frac{\frac{10}{2}}{100}\right )^{2 \times 2} $
=> 18000 $\displaystyle \left( 1 + \frac{5}{100}\right )^4 => 18000 \left(\frac{105}{100}\right )^{4} $
18000 $\displaystyle \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} = \frac{1750329}{80}$ = 21879.125 or Rs.21879.
Simple Interest = $\displaystyle \frac{25000 \times 15 \times 2}{100}$ = 7500.
Total amount = 25000 + 7500 = Rs.32500
Compound interest |
= |
25000 |
||
1st year @15% |
= |
3750 |
||
28750 |
||||
2nd year@15% |
= |
4312.5 |
||
Amount |
= |
33062.5 |
Difference => C.I – S.I = Rs.33062.5 – Rs.32500 = Rs.562.5
R = $\displaystyle \left((1.69)^{\frac{1}{2}} - 1 \right) \times 100$ = [1.3 – 1] x 100 = 30 or 30%
Difference = Rs.25088 – Rs.22400 = Rs.2688.
Rate = $\displaystyle \frac{2688}{22400} \times$ 100 = 12% => $\displaystyle \frac{22400}{100 + 12} \times 100$
Amount = $\displaystyle \frac{22400}{112} \times$ 100 = 20000.
Let Principal be 100.
Amount = P $\displaystyle \left(1 + \frac{\text{R}^3}{100}\right) = \frac{125}{64} = \left(\frac{5}{4}\right)^3 $
I. When Interest Compounded Annually:
1 + $\displaystyle \frac{\text{R}^3}{100} = \left(1 + \frac{\text{R}}{100}\right) = \frac{5}{4}$
$\displaystyle \frac{100\text{R}}{100} = \frac{5}{4}$ = 400R = 500 = R = $\displaystyle \frac{500}{400} \times$ 100 = 125.
As amount = Principal + interest
Rate = Amount – Principal = 125 – 100 = 25 or 25%
Let Principal be "P".
P $\displaystyle \left(1 + \frac{20}{100}\right)^2 - \left(1 + \frac{\frac{20}{2}}{100}\right)^4$ = Rs.723.
P $\displaystyle \left(\frac{12}{10}\right)^2$ - P $\displaystyle \left(\frac{11}{10}\right)^4$ = Rs.723.
$\displaystyle \frac{144\text{P}}{100} - \frac{121\text{P}}{100} \times \frac{121\text{P}}{100}$ = Rs.723.
Difference = 146.41 – 144 = 2.41 = Rs.723.
Sum = $\displaystyle \frac{723}{2.41} \times$ 100 = Rs.30000.
Principal = $\displaystyle \frac{\text{Difference}}{\text{R}^2} \times 100^2$
Principal or Sum = $\displaystyle \frac{900}{15 \times 15} \times 100 \times 100$ = Rs.40000.
Let principal be "P'.
I. When Interest Compounded Annually: (for two years)
Amount = P $\displaystyle \left(1 + \frac{\text{R}}{100}\right)^2$ = Rs.43200.
When Interest Compounded Annually: (for three years)
Amount = P $\displaystyle \left(1 + \frac{\text{R}}{100}\right)^3$ = Rs.51840.
$\displaystyle \frac{51840}{43200} = \frac{P \left(1 + \frac{\text{R}}{100}\right)^3}{P \left(1 + \frac{\text{R}}{100}\right)^2} = \frac{6}{5} = 1 + \frac{\text{R}}{100}$
$\displaystyle \frac{\text{R}}{100} = \frac{6}{5} - 1 = \frac{6 – 5}{5} = \frac{1}{5}$ or 20%.
Sum = P $\displaystyle \left(1 + \frac{20}{100}\right)^2$ = 43200.
= P $\displaystyle \left(\frac{120}{100}\right)^2$ = 43200.
= P $\displaystyle \left(\frac{6}{5}\right)^2$ = 43200 = P = $\displaystyle \frac{5}{6} \times \frac{5}{6} \times$ 43200 = Rs.30000.
[or] Direct:
51840 – 43200 = 8640
$\displaystyle \frac{8640}{43200} \times$ 100 = 20%, Compounded amount in third year is Rs.43200, then compounded amount in 2nd year =
$\displaystyle \frac{43200}{120} \times$ 100 = 36000.
Principal or Sum = $\displaystyle \frac{36000}{120} \times$ 100 = Rs.30000.
Let the amount be ‘P’, as it gets doubled for every 6 years, then
2 times in 6 years => 2P => in 12 years => 4P => 18 years => 8P
24 years => 16P or 16 times.
Descriptions | Status |
---|---|
Attempted Questions | |
Un-Attempted Questions | |
Total Correct Answers | |
Total Wrong Answers |
P = Principal => Is the amount Lent or Borrowed.
R = Rate of Interest => The extra amount payable on the Principal, from time to time or at a certain intervals.
n = Time => Is the period for which the amount is Lent or Borrowed. The time may be yearly, half yearly or quarterly.
Compound Interest: Interest accrued on Principal is again added to the principal and Rate of interest is calculated on accumulated or compounded amount, i.e this compounded amount again becomes principal.
A => is the total amount at the end of ‘n’ years.
I. When Interest Compounded Annually:
Amount = P $\displaystyle \left( 1 + \frac{\text{R}}{100}\right)^n $
II. When Interest Compounded Half Yearly:
Amount = P $\displaystyle \left( 1 + \frac{\frac{\text{R}}{2}}{100}\right)^{2n} $
III. When Interest Compounded Quarterly:
Amount = P $\displaystyle \left( 1 + \frac{\frac{\text{R}}{4}}{100}\right)^{4n} $
IV. When Interest Compounded Annually but time is in fraction, say 2 $\displaystyle \frac{1}{2}$ years.
Amount = P $\displaystyle \left( 1 + \frac{\text{R}}{100}\right)^{2} \times \left( 1 + \frac{\frac{1}{2} R}{100}\right) $
V. When Rates are different for different years. Say R_{1}%, R_{2}%, R_{3}% for 1st, 2nd and 3rd year respectively.
Amount = P $\displaystyle \left( 1 + \frac{\text{R}_1}{100}\right) \ \left( 1 + \frac{\text{R}_2}{100}\right) \ \left( 1 + \frac{\text{R}_3}{100}\right) $
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