Aptitude - Compound Interest - Discussion

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.

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.

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.

No @Garima.

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

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

Very good, Thanks everyone for explaining.

34347=30000(1+0.07)^n.
1.1449=(1.07)^n.
Using log in both the side.
log1.1449=n * log1.07.
n=log1.1449/log1.07.
n=2 years.

Verify with given option.
CI =7 %
1ST YEAR 7%.

For 2nd year, it becomes 7.49
Total 14.49
If 100% = 30K.
Then 114.49 = ?
(114.49 * 30K)÷100.

And you will get 4347.

How did come 11449?

Please, anyone, explain the answer in detail to me.