Question

I want the answer to these questions with method please!

Answer 1

(1) 

We know that A = P(1 + r/100)^n

Given amount after 2 years = 1210.

1210 = P(1 + r/100)^2  ----- (1)

Given amount after 5 years = 1610.51

1610.51 = P(1 + r/100)^5  ------- (2)


On solving (1) & (2), we get

1610.51/1210 = (1 + r/100)^3

1.331 = (1 + r/100)^3

$\sqrt[3]{1.331} = (1 + \frac{r}{100})$

$\sqrt[3]{1.331} - 1 = \frac{r}{100}$

$1.1 - 1 = \frac{r}{100}$

$0.1 = \frac{r}{100}$

r = 10% per annum.

Substitute r = 10 in (1), we get

1210 = P(1 + 10/100)^2

1210 = P(11/10)^2

P = 1210 * 10/11 * 10/11

   = 121000/121

   = 1000.


Hence the principal is 1000 and the rate of interest per annum = 10%.



(2)

Given that the interest is compounded semi-annually.

Given amount for 1 year = 8820. (1 year = 2 half-years, so n = 2)

8820 = P(1 + r/100)^2.   -------------- (1)

Given amount for 3/2 years = 9261.(3/2 years = 3 half-years, so n = 3).

9261 = P(1 + r/100)^3.   ----------------- (2)


Now,

On solving (1) & (2), we get

$\frac{9261}{8820} = 1 + \frac{r}{100}$

$\frac{21}{20} = 1 + \frac{r}{100}$

$\frac{21}{20} - 1 = \frac{r}{100}$

$\frac{1}{20} = \frac{r}{100}$

r = 5%.

Therefore Rate of interest = 5% per half-year and 10% per annum.


Now,

Subsitute r = 5% in (1), we get

8820 = P(1 + 5/100)^2

8820 = P(1 + 1/20)^2

8820 = P(21/20)^2

8820 = P(441/400)

P = 8820 * 400/441

P = 3528000/441

P = 8000.



Therefore the Sum is 8000 and Rate of interest is 10% p.a.


Hope this helps!