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Suniyo donated Rs. 2000 each to both Nobita and Giyan. If Giyan invested the money at 10% rate of interest at simple interest and Nobita gives the money to Doremon who put this money into a gadget that gives 11% rate of interest compounded annually then find after 2 years Nobita will get how much more interest than Giyan and also if they return the money to Suniyo then how much money Suniyo will get at the end of 2 years?

Suniyo donated Rs. 2000 each to both Nobita and Giyan. If Giyan invested the money at 10% rate of interest at simple interest and Nobita gives the money to Doremon who put this money into a gadget that gives 11% rate of interest compounded annually then find after 2 years Nobita will get how much more interest than Giyan and also if they return the money to Suniyo then how much money Suniyo will get at the end of 2 years? Correct Answer 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

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