Aptitude - Compound Interest - Discussion

Very good, Thanks everyone for explaining.

Can anyone please tell me how (1+7/100) become (107+100)?

No @Garima.

You should write it as 107/100 which came by the basic addition method.

Simple method :

Amount of Rs.30000 x 7/100 = 2100 first year
Next year we calculate compound interest so RS. 30000+2100 add the previous year's interest.
Rs.32100 x 7/100 = 2247 => second year interest.
First-year interest : Rs.2100
Second-year interest : Rs.2247
Total Rs.4347
So, the answer is 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.