A sum amounts to Rs.5445 in 2 years and to Rs.5989.50 in 3 years at CI Compounded Annually. Find the sum and rate of Interest. Also find the Compound Interest for 4 years at same rate for the same principal compounded Annually.

Solution(By Examveda Team)

Let principal was P and rate was r.
A = P* [1 + (r/100)]ⁿ
For Two years,
A = P * [1 + (r/100)]²
5445 = P * [1 + (r/100)]² -------------------- (1)
For three years,
A = P * [1 + (r/100)]³
5989.50 = P * [1 + (r/100)]³ --------------- (2)
Dividing equation (2) by (1)
5989.50 /5445 = P * [1 + (r/100)]³ /P * [1 + (r/100)]²
1.1 = 1 + r/100
r/100 = 0.1
r = 10%.
Putting the value of r in equation (1)
5445 = P * [1 + (10/100)]²
1.21P = 5445
P = Rs. 4500.

Amount after 4th year would be,
5989.50 + 10% of 5989.50 = Rs. 6588.45.
Interest added in 4 years = 6588.45 - 4500 = Rs. 2088.45.