 # Michael borrowed Rs 16000 from a finance company at $10 %$ per annum, compounded half-yearly.

Question:

Michael borrowed Rs 16000 from a finance company at $10 \%$ per annum, compounded half-yearly. What amount of money will discharge his debt after $1 \frac{1}{2}$ years?

Solution:

Principal amount $=$ Rs. 16000

Rate of interest $=10 \%$ per annum $=5 \%$ for half year

Time $=1 \frac{1}{2}$ years $=3$ half years

Principal for the first half year $=$ Rs. 16000

Interest for the first half year $=$ Rs. $\left(\frac{16000 \times 5 \times 1}{100}\right)=$ Rs. 800

Now, amount at the end of the first half year $=$ Rs. $(16000+800)=$ Rs. 16800

Principal for the second half year $=$ Rs. 16800

Interest for the second half year $=$ Rs. $\left(\frac{16800 \times 5 \times 1}{100}\right)=$ Rs. 840

Now, amount at the end of the second half year $=$ Rs. $(16800+840)=$ Rs. 17640

Principal for the third half year $=$ Rs. 17640

Interest for the third half year $=$ Rs. $\left(\frac{17640 \times 5 \times 1}{100}\right)=$ Rs. 882

Now, amount at the end of the third half year $=$ Rs. $(17640+882)=$ Rs. 18522

$\therefore$ The amount of money Michael has to pay the finance company after $1 \frac{1}{2}$ years is Rs $18522 .$