At a certain rate of simple interest, Rs.4050 amounts upto Rs.4526.50 in 2 years. At the same rate of simple interest, how much would 1 lakh amount in 3 years.
Let interest be i per annum simple interest.
4050(1+i*2)=4526.50
solve for i.
1+i*2=4526.5/4050=1.117654321
i=(1.117654321-1)/2
=0.058827
1 lakh = 100,000
So after 3 years, accumulated amount
=100,000(1+3i)
=100,000(1.1764815)
=117648.15
4526.5/4050 = 1.1176 or 11.76% in two years.
That means it gets 5.88% each year
so, 1 lakh grows by 0.0588 each year
...
To find the simple interest for 1 lakh in 3 years, we need to first determine the rate of simple interest.
We are given that Rs.4050 amounts to Rs.4526.50 in 2 years. To find the rate, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Here, the principal is Rs.4050, and the amount is Rs.4526.50. The time is 2 years.
Substituting these values into the formula, we have:
4526.50 = (4050 * Rate * 2) / 100
To find the rate, let's rearrange the formula:
Rate = (4526.50 * 100) / (4050 * 2)
Rate ≈ 5.58%
Now we can calculate the simple interest for 1 lakh in 3 years using the same rate of 5.58%.
Simple Interest = (Principal * Rate * Time) / 100
Principal = 1,00,000
Rate = 5.58%
Time = 3 years
Substituting these values into the formula, we have:
Simple Interest = (1,00,000 * 5.58 * 3) / 100
Simplifying the expression:
Simple Interest ≈ Rs.16740
Therefore, 1 lakh would amount to approximately Rs.1,16,740 in 3 years at the same rate of simple interest.