**Type iii** COMPUTATION OF COMPOUND INTERESTWHEN INTEREST IS COMPOUNDED QUARTERLY

It should be noted that, if the rate of interest is R % per annum and the interest is compounded quarterly, then it is R/4% per quarter.

**Example**

Find the compound interest on Rs 10000 for 1 year at 20% per annum compounded quarterly.

**Solution :** Rate of interest = 20% per annum = 20/4% = 5%

Time =1 year =4 quarters.

Principal for the first quarter = Rs 10000

Interest for the first quarter =

Amount at the end of first quarter = \( Rs 10000 + Rs 500 = Rs 10500 \)

Principal for the second quarter = \( Rs 10500 \)

Interest for the second quarter =\( Rs ( 10500*5*1/100) = Rs 525 \)

Amount at the end of second quarter = \( Rs 10500 + Rs 525 = Rs 11025 \)

Principal for the third quarter =\( Rs 11025 \)

Interest for the third quarter =\( Rs (11025*5*1/100) = Rs. 551.25 \)

Amount at the end of the third quarter = Rs 11025 + Rs 551.25 [/latex]

= Rs 11576.25

Principal for the fourth quarter = Rs 11576.25

Interest for the fourth quarter = \( Rs. ( 11576.25*5*1/100) = Rs. 578.8125 \)

Amount at the end of fourth quarter =\( Rs. 11576.25+Rs 578.8125 \)

= Rs 12155.0625

Compound interest = \( Rs 12155.0625 – Rs 10000 = Rs 2155.0625 \)

= Rs 2155.06