# Find the amount and the compound interest on Rs 10,000 for   years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

principal = 10000/-
rate of interest = 10% per annum
time = 1 1/2 years = 3 half yearly.
if compounded half yearly, amount = $10000*\left(1+\frac{10}{2*100}{\right)}^{3}$
$=10000*\left(1+\frac{1}{20}{\right)}^{3}\phantom{\rule{0ex}{0ex}}=10000*\frac{{21}^{3}}{{20}^{3}}\phantom{\rule{0ex}{0ex}}=10000*\frac{9261}{8000}\phantom{\rule{0ex}{0ex}}=11576.25/-$
thus interest = 11576.25 - 10000 = 1576.25/-
case II; if amount is compounded yearly.
amount at the end of 1st year = $10000*\left(1+\frac{10}{100}{\right)}^{1}=10000*\frac{11}{10}=11000/-$
interest for the half year = $\frac{11000*10*1}{100*2}=550/-$
thus the total interest when compounded annually
= (11000-10000)+550
=1000+550
=1550/-
thus the interest is more when compounded half yearly.
hope this helps you

• 7

(Compounded half - yearly)

P = Rs.10,000

T = 1 1/2 yrs. = 3/2 = 3/2 x 2 half years = 3 half years

R = 10% p.a. = 10/2% (for half years) = 5%

A = 10,000(1 + 5/100)^3

A = 10,000(105/100)^3

A = 10,000 x 105/100 x 105/100 x 105/100

A = 105 x 21 x 21 / 4

A = 46305 / 4

A = Rs.11576.25

C.I = Rs.11576.25 - Rs.10000 = Rs.1576.25

(On compounding annually)

P = Rs.10,000

R = 10%p.a

T = 1 1/2

Now, break it into 1 year and 1/2 year

For one year :

A = 10,000(1 + 10/100)^1

A = 10,000(110/100)^1

A = 10,000 x 110/100

A = 1000 x 11

A = Rs.11000

For half year : (S.I.)

1000 x 10 x 1 / 100 x 2

Rs.500

Total amount = Rs 11,000 + Rs.500 = Rs.11500

C.I. = Rs.11500 - 10,000 = 1500

C.I. compounded half-yearly = Rs.1576.25

C.I. compounded annually = Rs.1500

Therefore C.I. compounded half-yearly is more by Rs.76.25

• 1
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