Aptitude - Compound Interest - Discussion

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.

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.

30000*7/100 = 2100 for 1rst year.
For 2nd year : 30000+2100*7/100 = 2247.

Now, cross-check the given calculated amount given in the question itself i.e 4347 rupees by adding 2 years amount (2100+2247)=4347.

Believe this is the fastest and tricky method of our natural mind.

Simpler yet old-fashioned solution to me would be:

30000*7/100=2100 - year 1
30000+2100=32100*7/100=2247 - year 2
now add 2100+2247=4347 which was the compound interest earned after 2years.

Thus the ans is 2 years.

Sorry Guys but it should;

11449 / 10000 // 34347 / 30000 is multiplied and divide by 3.

Hence, Now 11449 and 10000 are squares of 107 and 100 resp.

Thus(107 / 100)^ 2. Thus n = 2.

C.I will be the 4347.

C.I = AMOUNT-PRINCIPAL.

PRINCIPAL = 30,000.

4347 = AMOUNT-30000.

AMOUNT = 4347+30000 = 34347.

AMOUNT = P(1+R/100)^n.

34347 = 30000(1+7/100)^n.

34347/30000 = (107/100)^n.

Use the formula

n = [ log(fv/p) ] / [ log (1+i)].

Where
FV = future value.
P = present value.
i = interest ( in dec. place).

n = [ log ( 34,347/30,000) ] / [ log (1+0.07)].
= 2.

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.

11449/10000 = (107/100)^n , 1.1442 = (1.07)^n.

We can write as log 1.1442 = n log 1.07, n = log 1.1442/log 1.07 = 0.058501/0.029383 = 2 (as per scientific calculator).