Question

For how many years do we need to invest a principal of Rs. 30,000 in a company to
make it amount to Rs. 90,000 at an annual rate of interest of 67 t is given that the
interest is compounded annually.
Also, log 106 = 2.025 and log 3 = 0.4771​

Answer 1

Answer:

A = p(1+r/100) ^n

90000 = 30000 (1 + 6/100) ^ n

log3 = n (log 106/100)

0.4471 = n (log 106 - 2log 100)

0.4771 = n( 2.025 - 2)

n = 0.4771 / 0.025

= 19.084

Answer 2

19 years do we need to invest a principal of Rs. 30,000 in a company to make it amount to Rs. 90,000.

For how many years do we need to invest a principal of Rs. 30,000 in a company to make it amount to Rs. 90,000 at an annual rate of interest of 6 % ?

It is given that the interest is compounded annually.

[ Also, log 106 = 2.025 and log 3 = 0.4771 ]

We know,

$\quad A=P\left(1+\frac{r}{100}\right)^n$

here,

• A = Rs. 90,000
• P = Rs. 30,000
• r = 6 %

⇒ 90000 = 30000(1 + 6/100)ⁿ

⇒3 = (106/100)ⁿ

taking log base 10 both sides , we get,

⇒log3 = n log(106/100)

⇒log3 = n [log(106) - log(100)]

Given,

• log3 = 0.4771
• log(106) = 2.025
• log100 = log10² = 2log10 = 2 × 1 = 2

⇒0.4771 = n(2.025 - 2)

⇒0.4771 = n × 0.025

⇒n = 0.4771/0.025 = 19.084 ≈ 19 years (approx)

Therefore 19 years do we need to invest a principal of Rs. 30,000 in a company to make it amount to Rs. 90,000.