Mathematics

If the letters have usual meanings, the formula for finding compound interest, compounded yearly for the given time is :
$1\dfrac{1}{2}$ years :
$P\Big[\Big(1 + \dfrac{r}{100}\Big)^{1\dfrac{1}{2}}- 1\Big]$
$P\Big(1 + \dfrac{r}{100}\Big)\Big(1 + \dfrac{r}{200}\Big)$ - P
$P\Big(1 + \dfrac{r}{200}\Big)^3$
$P\Big(1 + \dfrac{r}{100}\Big)^3\Big(1 + \dfrac{r}{200}\Big)- P$

Compound Interest

6 Likes

Answer

Let sum = ₹ P.

Amount for first year :

A = $P\Big(1 + \dfrac{r}{100}\Big)^1$

For next $\dfrac{1}{2}$ year :

Sum = ₹ $P\Big(1 + \dfrac{r}{100}\Big)$

A = $P\Big(1 + \dfrac{r}{100}\Big)\Big(1 + \dfrac{r}{2 \times 100}\Big)^{\dfrac{1}{2} \times 2} = P\Big(1 + \dfrac{r}{100}\Big)\Big(1 + \dfrac{r}{200}\Big)$

By formula,

C.I. = A - P = $P\Big(1 + \dfrac{r}{100}\Big)\Big(1 + \dfrac{r}{200}\Big) - P$

Hence, Option 2 is the correct option.

Answered By

3 Likes

Mathematics

Compound Interest

Answer

Related Questions

A certain sum of money amounts to ₹ 23400 in 3 years at 10% per annum simple interest. Find the amount of the same sum in 2 years at 10% p.a. compound interest.

Mohit borrowed a certain sum at 5% per annum compound interest and cleared this loan by paying ₹ 12600 at the end of the first year and ₹ 17640 at the end of the second year. Find the sum borrowed.

If the letters have usual meanings, the formula for finding compound interest, compounded yearly for the given time is :
1 year :
$P\Big(1 + \dfrac{r}{100}\Big)^1 - P$
$P\Big(1 + \dfrac{r}{200}\Big)$ - P
$P\Big(1 + \dfrac{1}{200}\Big)^2$ - P
$P\Big(1 - \dfrac{r}{200}\Big)^2$ - P