An amount of Rs. 'Z' is invested in two different schemes—one offers simple interest at 13% p.a. for 4 years, and the other offers compound interest at 12% p.a. compounded annually for 2 years. If the total amount from the simple interest scheme exceeds the compound interest scheme by Rs. 78, then find the value of Z.
Show answer & explanation
Correct answer: B
Explanation
Given:
Investment = Rs. x
Simple Interest Scheme: Rate = 13%, Time = 4 years
Compound Interest Scheme: Rate = 12%, Time = 2 years
Difference = Rs. 78
As per the formula:
Simple Interest Amount = P(1 + rt/100)
Compound Interest Amount = P(1 + r/100)²
Simple Interest Amount = x(1 + 13 × 4/100) = 1.52x
Compound Interest Amount = x(1 + 12/100)²
= x(1.12)²
= 1.2544x
Difference = 78
1.52x − 1.2544x = 78
0.2656x = 78
x = 78 / 0.2656
x = 293.66