Question

At what rate percent a sum of rs.1600 amounts to rs.1933 after 2 years if interest is compounded half yearly

Answer 1

here is ur answer guy

Answer 2

The rate percent is 4.14%.

Step-by-step explanation:

Given : A sum of Rs.1600 amounts to Rs.1933 after 2 years if interest is compounded half yearly.

To find : At what rate percent ?

Solution :

The amount formula is given by,

$A=P(1+\frac{r}{n})^{nt}$

Where, A is the amount A=Rs.1933

P is the principal P=Rs.1600

r is the interest rate

t is the time t=2

n is the compounded year n=2

Substitute the value,

$1933=1600(1+\frac{r}{2})^{2\times 2}$

$\frac{1933}{1600}=(1+\frac{r}{2})^{4}$

$1.208125=(1+\frac{r}{2})^{4}$

Taking log both side,

$\log(1.208125)=4\log(1+\frac{r}{2})$

$\frac{\log(1.208125)}{4}=\log(1+\frac{r}{2})$

Taking antilog,

$e^{\frac{\log(1.208125)}{4}}=1+\frac{r}{2}$

$1.0207=1+\frac{r}{2}$

$\frac{r}{2}=0.0207$

$r=0.0414$

Converting into percentage,

$r=0.0414\times 100$

$r=4.14\%$

Therefore, the rate percent is 4.14%.

#Learn more

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