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Formulas for Compound Interest Problems

Formulas for Compound Interest in Aptitude

Compound interest is the interest on interest to the principal sum of a amount. It is calculated by  result of reinvesting interest, rather than paying it out. By this interest in the next period is  earned on the principal sum plus previously accumulated interest.

Formulas For Compound Interest CI

Compound Interest Formulas

  • Compound interest is the interest calculated on the original principal and on the accumulated past interest of a deposit or loan. Compound interest is calculated based on the principal, interest rate (APR or annual percentage rate), and the time involved.

Formula of Compund Interest (CI) =  P (1+ \mathbf{\frac{r}{100}})^{n} – P

Formula of  Amount     =    CI +P

=   P (1+ \mathbf{\frac{r}{100}})^{n} – P + P

Here,  P = Principal

  r = rate of interest

  t = the number of years the amount is deposited or borrowed for.

  n= the number of times that interest is compounded per unit ‘t’.

 

Formula of compound Interest

Formulas for Compound Interest

 

  • Formulas for Compound Interest (When Interest is Compound Annually)
    • Amount = P\mathbf{(1+ \frac{r}{100})^{n}}
    • Compound Interest =Total amount – Principal
    • Rate of interest (R) = [\mathbf{(\frac{A}{P})^{\frac{1}{t}}}− 1]%

 

  • Formulas of Compound Interest (When Interest is Compound Half Yearly)
    • Amount = P (1+ \mathbf{\frac{{\frac{r}{2}}}{100})^{2n}}
    • Compound Interest = Total amount – Principal

 

  • Compound Interest Formulas (When Interest is Compound Quarterly)
    • Amount = P (1+ \mathbf{\frac{{\frac{r}{4}}}{100})^{4n}}
    • Compound Interest = Total amount – Principal

 

  • Formulas of Compound Interest (When Interest is Compound Monthly)
    • Amount = P (1+ \mathbf{\frac{{\frac{r}{12}}}{100})^{12n}}

 

  • Compound Interest Formulas (When Interest is Compounded Annually but time is in fraction, say 2(\mathbf{\frac{3}{2}})years )
    • Amount = P (1+ \mathbf{\frac{r}{100}})^{2}(1+ \mathbf{\frac{\frac{3}{2}r}{100}})

 

  • Formulas of Compound Interest (When rates are different for different years)
    • Amount = P (1+\frac{r_{1}}{100}) (1+\frac{r_{2}}{100}) (1+\frac{r_{3}}{100})

 

  • Formulas for Compound Interest (Present worth of Rs. x due n years)
    • Present worth =    \frac{x}{(1+\frac{r}{100})}

Problems Based on Formulas Of  Compound interest with solutions

 

Question 1 . Find the amount on Rs 16000 for 3 year at 5% per annum compounded annually n.

[A] Rs. 18562

[B] Rs. 18550

[C] Rs. 18952

[D] Rs. 18552

Solution :     According to the formula of Compound Interest

Amount = P (1+ \mathbf{\frac{r}{100}})^{n}

Amount = 16000 (1+ \mathbf{\frac{5}{100}})^{3}

Amount = 16000 (1+ \mathbf{\frac{1}{20}})^{3}

Amount = 16000 (\mathbf{\frac{21}{20}})^{3}

Amount =18552

 

Question 2 . Find the  compound interest on Rs. 10,000 at 20% per annum for 5 years 4 months, compounded annually is :

[A] Rs. 16600

[B] Rs. 16544

[C] Rs. 15644

[D] Rs. 16500

Solution :    According to the Formula of Compound Interest ,

CI = P (1+ \mathbf{\frac{r}{100}})^{n} – P

CI = 10,000 (1+ \mathbf{\frac{20}{100}})^{5\frac{1}{3}} – 10,000
 
CI = 10,000 (1+ \mathbf{\frac{1}{5}})^{5\frac{1}{3}} – 10,000
 
CI = 10,000 (1+ \mathbf{\frac{1}{5}})^{5}(1+ \mathbf{\frac{1}{3*5}}) – 10,000
 
CI = 10,000 (1+ \mathbf{\frac{1}{5}})^{5}(1+ \mathbf{\frac{1}{3*5}}) – 10,000
 
CI = 10,000 (1+ \mathbf{\frac{1}{5}})^{5}(1+ \mathbf{\frac{1}{15}}) – 10,000
 
CI = 10,000 (\mathbf{\frac{6}{5}})^{5}(\mathbf{\frac{16}{15}}) – 10,000
 
On Solving ,
 
CI = 26544 – 10,000
 
CI = 16544