You need to borrow some money, so you take out a loan. One bank offers a 4% APR compounded quarterly, while another bank offers a 4% APR compounded monthly. Which one would you choose? Justify your answer with a short explanation.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.1: Exponential Functions
Problem 53E: Interest Ron Hampton needs to choose between two investments: One pays 6% compounded annually, and...
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You need to borrow some money, so you take out a loan. One bank offers a 4% APR compounded quarterly, while another bank offers a 4% APR compounded monthly. Which one would you choose? Justify your answer with a short explanation.
Expert Solution
Given,

One bank offers a 4% APR compounded quarterly, while another bank offers a 4% APR compounded monthly. 

Let P be the amount taken as loan.

Now at 4% APR compounded quarterly, we get

A=P1+rnnt=P1+0.0444t=P1.014t

Now at 4% APR compounded monthly, we get

A=P1+rnnt=P1+0.041212t=P1.003312t

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