1 Answers
Option 3 : Rs. 64.20 and Rs. 4864.20
Given:
Giyan got Rs. 2000 and invested this money at a rate of 10% for 2 years on simple interest.
Nobita also gets Rs. 2000 and invests this money at a rate of 11% for 2 years on compound interest.
Concept:
We will calculate the individual rate of interest for both Giyan and Nobita and then find the difference between them.
Formula used:
Simple interest (SI) = (Principal (P) × Rate (R) × Time (T))/100
⇒ SI = (P × R × T)/100
And in compound interest (CI),
Amount (A) = P (1 + R/100)T
CI = A – P
Successive increase = x + y + (x × y)/100
Where x and y are two rates of interest.
Calculation:
Interest of Giyan
SI = (2000 × 10 × 2)/100 = 400
So, Giyan will get Rs. 400 as interest
For Nobita,
A = 2000 × (1 + 11/100)2
⇒ A = 2000 × 111 × 111/10000 = 2 × 12321/10 = 2464.2
CI = 2464.2 – 2000 = 464.2
∴ Nobita will get Rs. 64.20 extra interest from Giyan.
∴ The total amount received by Suniyo after 2 years = 2000 + 2000 + 400 + 464.2 = Rs. 4864.20
Short trick:
SI for 2 years at a rate of 10% = 2 × 10 = 20% = Rs. 400
CI for 2 years at a rate of 11% = 11 + 11 + (11 × 11)/100 = 23.21% = Rs. 464.20
∴ Nobita will get 3.21% extra interest i.e. = 3.21 × 2000/100 = Rs. 64.20
∴ The total amount received by Suniyo after 2 years = 2000 + 2000 + 400 + 464.2 = Rs. 4864.20