Question
A certain sum was invested at simple interest. After 5
years, it became (117/ ninety) times the amount it had reached in 3 years. Find the annual rate of interest.Solution
ATQ,
Let the rate of interest be βr%β p.a.
Let the amount after 3 years = Rs. β90xβ
So, amount after 5 years = (117/90) Γ 90x = Rs. β117xβ
Interest in 2 years = 117x β 90x = Rs. β27xβ
So, yearly interest = 27x / 2 = Rs. β13.5xβ
Principal = 90x β 13.5x Γ 3 = Rs. β49.5xβ
ATQ,
49.5x Γ (r / 100) Γ 1 = 13.5x
r = (13.5x Γ 100) / 49.5x = 27.27
The rate of interest = r = 27.27%
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