Compound Interest

Rita Lamichhane

Student

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At what rate of compound interest per annum, a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?

  • 23 Dec, 2023
Replies (2)
Vidhyamath Online

Instructor

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Solution:

Let R% be the rate of interest per annum.

Given,

Principal (P) = Rs. 1200

Total amount after 2 years (A) = Rs. 1348.32

T = 2

We know that,

A = P[1 + (R/100)]T

Rs. 1348.32 = Rs. 1200[1 + (R/100)]2

1348.32/1200 = [1 + (R/100)]2

[1 + (R/100)]2 = 134832/120000 [1 + (R/100)]2 = 2809/2500 [1 + (R/100)]2 = (53/50)2

1 + (R/100) = 53/50

R/100 = (53/50) – 1

R/100 = (53 – 50)/50

R = 300/50

R = 6

Hence, the rate of interest is 6%.


Note:

Amount, when interest is compounded half-yearly, is

A = P[1 + (R/200)]2T

Here,

R/200 = half-yearly rate

2T = the number of half years

  • 23 Dec, 2023

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