What is the compound interest on Rs 8000 for 1 year at 10% pa payable half yearly?

Find the amount and the compound interest on Rs 8000 for \[1\frac{1}{2}\] years at 10% per annum, compounded half-yearly.

Solution

Given: 
P = Rs 8, 000
R = 10 % p . a . 
n = 1 . 5 years
When compounded half - yearly, we have: 
\[A = P \left( 1 + \frac{R}{200} \right)^{2n} \]
\[ =\text{ Rs }8, 000 \left( 1 + \frac{10}{200} \right)^3 \]
\[ =\text{ Rs }8, 000 \left( 1 . 05 \right)^3 \]
 = Rs 9, 261
Also, 
CI = A - P
 = Rs 9, 261 - Rs 8, 000
 = Rs 1, 261

Calculate the amount and compound interest on Rs 8,000 for 1 year at 9% per annum compounded half yearly.

Here P = Rs 8000,   T = 1 year,    R = 9% p.a.

Interest is compounded half yearly,

∴       T = 1 year = 2 half years

         R = 9% p.a.=

∵         Amount =

                     = Rs 8000

                     = Rs.

                                          = Rs

                              CI = Rs 8736.20 - Rs 8000

                      = Rs 736.20

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