A person deposited a sum of money in a bank providing simple interest and the same amount in another bank which offered compound interest at the same rate. The ratio of the differences in the simple interest and compound interest after 2 and 3 years was 4 : 13. Find the rate of interest.?

14%
15%
25%
26%

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 3 : 25%

As not mentioned we assume that interest is compounded annually so n = 1.

After 2 years,

S.I. = prt = 2pr

C.I. = p(1 + r/n)^nt – p = p(1 + r)² – p = p(2r + r²)

C.I. – S.I. = pr²

After 3 years,

S.I. = prt = 3pr

C.I. = p(1 + r / n)^nt – p = p(1 + r)³ – p = p(r³ + 3r² + 3r)

C.I. – S.I. = p(r³ + 3r²)

Ratio = r²/ (r³ + 3r²) = 4 / 13

⇒ 13r² = 4r³ + 12r²

⇒ r² = 4r³

⇒ r = 1 / 4 = 25%

∴ rate of interest is 25%.

4 views Answered 2022-09-04 04:29

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