Q. 84.3( 72 Votes )

# Arif took a loan of Rs. 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after 1years, if the interest is compounded annually and compounded half yearly.

Answer :

For compounded Annually

Principal (P) = Rs. 80000

Time period (n) = 1

Rate of interest (R) = 10%

= 80000×1.05^{3}

= 88000

∴ Amount for 1 year = Rs. 88000

Interest for remaining 6 months =

= 4400

∴ Amount for 1.5 years = Rs. 88000+4400 = Rs. 92400

= 92400-80000

∴ Compound Interest = Rs. 12400

For compounded half yearly

Principal (P) = Rs. 80000

Time period (n) = 3

Rate of interest (R) for half year = 10%× = 5%

= 80000×1.05^{3}

= 92610

∴ Amount = Rs. 92610

= 92610-80000

∴ Compound Interest = Rs. 12610

∴ the difference in amounts = amount for For compounded half yearly - amount for For compounded annually

= 92610-92400

= Rs. 210

∴ The difference in amounts is Rs. 210

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