How do you solve for You are considering options from two roofing contractors to

Question

How do you solve for

You are considering options from two roofing contractors to fix your roof. Option A will last you 12 years and cost $5,300 whereas Option B will last 24 years and cost $8,200. If you are planning to take a home equity loan from your bank, at what interest rate would you be indifferent to the two options. (Hint: Use Goal Seek)

5.15%

You are considering options from two roofing contractors to fix your roof. Option A will last you 12 years and cost $5,300 whereas Option B will last 24 years and cost $8,200. If you are planning to take a home equity loan from your bank, at what interest rate would you be indifferent to the two options. (Hint: Use Goal Seek)

5.15%

Explanation / Answer

Let r be the interest rate

EUAC for Option A=5300*r/(1-1/(1+r)^12)

EUAC for Option B=8200*r/(1-1/(1+r)^24)

In excel,

write in Cell B1 1%

write in Cell D5=5300*B1/(1-1/(1+B1)^12)

write in Cell D6=8200*B1/(1-1/(1+B1)^24)

write in Cell D7=D5-D6

Go to Data Tab->What if ANalysis->Goal Seek

Set Cell D7

To value 0

By Changing Cell B1

We get value of B1=5.15334047323671%

hence, r=5.15334047323671%

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