GATE CE 2024 Set 2 — Question 47
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Engineering Mathematics → Calculus → Limits & Continuity
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Question
The expression for computing the effective interest rate () using continuous compounding for a nominal interest rate of 5% isThe effective interest rate (in percentage) is ____________ (rounded off to 2 decimal places).
Correct answer
5.11 to 5.15
Solution
The effective interest rate () for continuous compounding is derived from the limit definition of the exponential function:where is the nominal interest rate.Given the nominal interest rate , we substitute this into the formula:Using the value of :To express the effective interest rate as a percentage:Rounding off to two decimal places, we get 5.13%. The official range provided is 5.11 to 5.15.
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