Question

in what time will the interest on a certain sum of the money at 7% be 11/4of itself​

Answer 1

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Let say it happens after n years

Case 1 : Compound interest Annually -

Then Interest = P * (1 + 7/100)ⁿ - P

Interest = 11P/4

11P/4 = P * (1 + 7/100)ⁿ - P

=> 15P/4 = P * (1 + 7/100)ⁿ

=> (1.07)ⁿ = 15/4

Taking log both sides

=> n log(1.07) = log(15/4)

=> n = 19.5 years

Case 2 Simple Interest

11P/4 = P * 7 * n /100

=> n = 1100/28

=> n = 39.3 Years

Case 3 : Amount becomes = 11P/4 after n years at simple interest

then interest = 11P/4 - P = 7P/4

7P/4 = P * 7 * n/100

=> n = 25 years

So correct Question Should be

In what time will the amount on a certain sum of money at 7% (simple interest) be 11/ 4 ( 2 whole 3 / 4 ) of itself

Answer 2

Answer:

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Let say it happens after n years

Case 1: Compound interest Annually - Interest = 11P/4

Then Interest=P*(1 + 7/100)n - P

11P/4 =P*(1 + 7/100) - P

=> 15P/4

=

P*(1 + 7/100)^

=> (1.07)n = 15/4

Taking log both sides

=> n log(1.07) = log(15/4)

=> n = 19.5 years

LTE l 63D

Case 2 Simple Interest

11P/4 =P* 7 *n/100

=> n = 1100/28

=> n = 39.3 Years

Case 3 : Amount becomes = 11P/4 after n years at simple interest then interest = 11P/4 - P = 7P/4

7P/4 =P*7* n/100

=> n = 25 year

So correct Question Should be

In what time will the amount on a certain sum of money at 7% (simple interest) be 11/ 4 (2 whole 3/4) of itself