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Rohit borrowed ₹ 40,000 for 2 years at 10% per annum C.I. and Manish borrowed the same sum for the same time at 10.5% per annum simple interest. Which of these two gets less interest and by how much?

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#### Solution

Sum borrowed (P) = ₹40000

Rate (R) = 10% p.a. compounded annually

Time (T) = 2 years

∴ Interest for the first year =`"PRT"/100`

`=₹(40000xx10xx1)/100`

= ₹4000

Amount after one year = ₹40000 + 4000

= ₹44000

Principal for the second year = ₹44000

∴ Interest for the second year

`=(44000xx10xx1)/100`

= ₹4400

∴ Compound Interest for 2 years = ₹4000 + 4400

= ₹8400

In the second case,

Principal (P) = ₹40000

Rate (R) = 10.5% p.a.

Time (T) = 2 years

∴ Simple Interest = `"PRT"/100=(40000xx10.5xx2)/100`

`=₹(40000xx105xx2)/(100xx10)`

= ₹8400

In both the cases, interest is same.