Question

If interest is compounded every six months a principal of Rs. 8,000 at 10% rate of interest will amount to at the end of 18 months.
A) Rs. 9,000
B) Rs. 9,156
C) Rs. 9,261
D) Rs. 9,282
Please explain step by step...

Answer 1

Answer:

9261/-

Step-by-step explanation:

We know that,

A= P( 1 + r/100 ) n

= A = 8000 ( 1 + r/2/100 ) 2n. { when compounded half yearly r/2 and 2n )

=> A = 8000 ( 1 + 10/200 ) 2 × 3/2

= 8000 × ( 210 / 2000 ) 3

= 8000 × 210/200 × 210/200 × 210/200

= 21 × 21 × 21

A = 9261 rs.

Answer 2

Answer:

Concept:

Compound interest is interest on a loan or deposit calculated on the basis of the initial principal and accumulated interest from previous periods. Believed to have originated in Italy in the 17th century, compound interest can be thought of as "interest on interest". This will cause the amount to grow faster than simple interest, which is calculated on the principal amount only.

The rate at which compound interest accrues depends on the frequency of compounding. The higher the number of compounding periods, the greater the compound interest. For example, the amount of compound interest accrued on $100 compounded at 10% annually will be less than $100 compounded at 5% semiannually over the same time period.

Find:

Find an amount to at the end of 18 month

Given:

If interest is compounded every six months a principal of Rs. 8,000 at 10% rate of interest will amount to at the end of 18 months.

Step-by-step explanation:

Principal sum = Rs. 8000

Rate = 10%

Interest is calculated half-yearly,

So, Rate, R = 10/2 =5%

Time 18 month = 3 half years, So, n = 3

$Amount = Principal x (1 + \frac{r}{100)})^{n}$

$Amount = 8000 × (1+ \frac{5}{100} ) ^{3}$

$Amount = 8000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20}$

Amount = Rs. 9261

Compound interest = Amount - Principal

Compound interest = 9261 - 8000

Compound interest = Rs. 1261

Hence the compound interest is 1261