Aptitude - Compound Interest - Discussion

Thanks, friends. It helped a lot!

Shortcut through using ln:

t = ln (34 347/30 000)/ln (1.07).
t = 2 years.

To find the period in years, we need to use the formula for compound interest:

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

Where:
A = Final amount.
P = Principal amount (Rs. 30,000).
r = Annual interest rate (7% or 0.07).
n = Number of times the interest is compounded per year (Generally compounded annually, so n=1)
t = time in years.

Given:
Compound interest (CI) = Rs. 4347.
Principal amount (P) = Rs. 30,000.
Rate of interest (r) = 7% or 0.07.
Number of times compounded per year (n) = 1.

We have to find time, t.

First, let's calculate the final amount using the formula:

A = P(1 + r/n)^(nt).
A = 30000(1 + 0.07/1)^(1*t).
4347=30000(1.07)^t.

Now, we solve for t by converting it into a logarithmic form by taking log on both sides.

log4347/log30000 = log(1.07)^t.
log((4347/30000) = log((1.07)^t).
t = log((4347/30000))/(log(107)).
t = 3 years.

Given.

Compound interest = 7%.
Principle amount = 30000.
The final amount after receiving the interest is 4347.
So calculate the interest for the first year.
= 30000/100 * 7 = 2100 rs.

Now, calculate the compound interest.
for 1 year = 2100.
for 2 year= 2247.
for 3 year = 157.29.

Now add those.
2100 + 2247 + 157.29.
So the addition of the first two interest answer is 4347.
That is why the answer is 2.

What is the shortcut method for calculating the square root of 11449?

Can any one please help how it has come (107/100)^2

Yaa, its because (107)^2 = 11449 and (100)^2 = 10000.

What is 107/100 ?

Amount=30000+4347 = 34347
amount=p(1+R/100)^n
34347=30000(1+7/100)^n
34347=30000(107/100)^n
34347/30000=(107/100)^n
11429/10000=(107/100)^n.
hence
(107/100)^2=11429/10000.

4347=30,000(1+7/100)^n why not?
and 30,000+4347=34,347 why?
plz any one explian me.