On a sum, simple interest at the annual rate of 12 percent for 6 years is Rs. 28800. What will be the compound interest on the same sum at the annual rate of 20 percent (compounding annually) for 2 years? 

Given:

Simple interest on a sum at 12% for 6 years = Rs. 28800

The annual rate for compound interest is = 20%

Time for compound interest = 2 years

Concept used:

Compound interest is calculated on the simple interest and interest on the sum.

Formula used:

\({SI}\ =\ {P× R× T\over 100}\)

\({CI}=\ {P\ × [(1+{R\over100})^T\ -\ 1]}\)

Where, SI = Simple interest, CI = Compound interest, P = Principle, R = Rate, and T = Time

Calculate:

Let the sum be X.

According to the question

⇒ \({28800}\ =\ {X × 12\ × 6\over 100}\)

⇒ 28800 × 100 = 72X

⇒ X = 400 × 100 = 40000

The compound interest.

\({CI}=\ {40000\ × [(1+{20\over100})^2\ -\ 1]}\)

 \({CI}=\ {40000\ × [{({100+20\over100})^2}\ -\ 1]}\)

\({CI}=\ {40000\ × [{({120\over100})^2}\ -\ 1]}\)

\({CI}=\ {40000\ × [{({6\over5})^2}\ -\ 1]}\)

\({CI}=\ {40000\ × [{({36\over25})}\ -\ 1]}\)

\({CI}=\ {40000\ × [{36\ -\ 25\over 25}]}\)

\({CI}=\ {40000\ × [{36\ -\ 25\over 25}]}\)

\({CI}=\ {40000\ × [{11\over 25}]}\)

\({CI}=\ {40000\ × [{11\over 25}]}\) = 17600

∴ The compound interest is 17600.