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You are considering moving your money to new bank offering a​ one-year CD that pays an 5 %5% APR with monthly compounding. Your current​ bank's manager offers to match the rate you have been offered. The account at your current bank would pay interest every six months. How much interest will you need to earn every six months to match the​ CD?

Answer :

TaeKwonDoIsDead

Answer:

2.53%

Explanation:

We need to understand what effective annual rate is to solve this question.

Effective Annual Rate is the actual interest earned on an investment due to effect of compounding.

The formula is:

Effective Annual Rate = [tex](1+\frac{i}{n})^n - 1[/tex]

Where

i is the interest rate given (nominal interest rate)

n is the number of compounding per year

For the old bank,

5% is the interest rate, so i = 5% = 5/100 = 0.05

n is the number of compounding per year, that will be n = 12 since compounding monthly

So, we have:

Effective Annual Rate [tex](1+\frac{0.05}{12})^{12} -1\\=0.051161[/tex]

For second bank, we have:

i = what we need to find

n = 2 (since semi annual compounding, every 6 months)

So,

Effective Annual Rate = [tex](1+\frac{i}{2})^2 - 1[/tex]

This should be equal to APR from 1st bank (0.05)

So, we solve for i:

[tex]0.05=(1+\frac{i}{2})^2 - 1\\1.05=(1+\frac{i}{2})^2 \\i=0.0253[/tex]

So, the interest would have to be

0.0253 * 100 = 2.53%

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