Question

Ashok borrowed 12000 at some rate percent compound interest. After a year he paid 4000.If C.I. for second year be 920,find rate of interest charged

Answer 1

||✪✪ GIVEN ✪✪||

• Borrowed Money = Rs.12000
• After 1 year Ashok Paid = Rs.4000
• CI for 2nd year = Rs.920

|| ★★ CONCEPT USED ★★ ||

• Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as interest on interest.

• But, Here we won’t use the Formula of Compound Interest. we will use Simple Interest Formula Only.

• ∙Interest on First Year of Simple Interest and Compound Interest are always equal.

• ∙Principal for Compound interst for next consecutive years can be find by Adding Principal and Past Year Interest..

|| ✰✰ ANSWER ✰✰ ||

Let us Assume That, Rate of Interest was R% per annum compounded Annually .

So, CI of First years = SI of First Year.

➪ SI = (P * R * T )/100

Putting values we get,

➪ SI = (12000 * R * 1)/100

➪ SI = 120R .

So,

➼ Amount After 1 year = Principal + SI .

➼ Amount = (12000 + 120R)

_______________________

Now, He Paid Rs.4000 .

So,

➳ Left Amount = (1200 + 120R) - 4000

➳ Left Amount = (8000 + 120R)

_______________________

Now, CI on This Amount Will also be same Like SI at same Rate .

So,

➺ SI = [ (8000 + 120R) * R * 1 ] / 100

➺ SI = (800R + 12R²) / 10

______________________

Now, we Have Given That, C.I. for second year be Rs.920,

So, Comparing Now, we get,

⟿ (800R + 12R²) / 10 = 920

⟿ (800R + 12R²) = 9200

⟿ 12R² + 800R - 9200 = 0

⟿ 4(3R² + 200R - 2300) = 0

⟿ 3R² + 200R - 2300 = 0

Splitting The Middle Term Now :-

☛ 3R² - 30R + 230R - 2300 = 0

☛ 3R(R - 10) + 230(R - 10) = 0

☛ (R - 10)(3R + 230) = 0

Putting Both Equal To Zero , we get,

☞ (R - 10) = 0

☞ R = 10%

Or,

☞ (3R + 230) = 0

☞ 3R = (-230)

☞ R = (-230/3) % ⟪ Negative Rate ≠ ⟫ .

•°• Required Rate of Interest is 10% Per Annum.

Answer 2

Refer The Attachment........