Question

On a sum of 6400 earns compound interest of 1008.80 rate of interest is 10% reckoned half-yearly. find time

Answer 1

Answer:

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Given: A sum of ₹6,400 earns a compound interest of ₹1,008.80 in 18 months, when the interest is reckoned half-yearly. Find the rate of interest.

Principal = Rs. 6400

Interest = 1008.80

Period = 18 months = 18 / 12 = 3 / 2 years

Interest reckoned half-yearly.

Amount = principal + interest = 7408.80

Substituting the values in the compound interest formula, we get:

A = P (1 + r/n)^nt

7408.80 = 6400 (1 + r/2)^(2*3/2)

7408.80 / 6400 = (1 + r/2)^3

1.157625 = (1 + r/2)^3

1 + r/2 = cube root of 1.157625 = 1.05

r/2 = 0.05

Therefore r = 0.1

Rate of interest = 0.1 * 100 = 10%

Thank you.

Answer 2

Answer:

The sum of money 6400 earns with compound interest of 1008.80 in 9 months at rate of interest 10%.

Step-by-step explanation:

Given:

Principle, P $=6400$

Compound interest $=1008.80$

Sum of money, A = Principle+ Compound interest

$A=6400+1008.80\\A=7408.80$

We know the formula, $A=P(1+\frac{r}{100} )^{n}$

where r is rate of interest and n is number of half years.

Given, rate of interest r = 10%

Therefore, $7408.80=6400(1+\frac{10}{100} )^{n}$

$\frac{7408.80}{6400}=(1+0.1} )^{n}$

$1.1576=(1.1)^{n}$

∴   $n=1.5$

Now, number of months $=1.5*6=9months$

Therefore, the time will be nine months.