Question

In: Finance

You currently have a 30-year mortgage with annual payments of $6000. Annual interest rate is 8%....

You currently have a 30-year mortgage with annual payments of $6000. Annual interest rate is 8%. In how many years, the balance on your mortgage will drop to half of its current value? Round your result to two decimal places (i.e., if the result is 7.6542, enter it as 7.65).

Solutions

Expert Solution

Annual Payment = $6000

First, we will calculate the Principal Loan amount:-

Where, P= Loan amount

r = Periodic Interest rate = 0.08

n= no of periods =30

Loan Amount = $ 67,546.70

Now, Calculate the no of period that will make the loan balance to be half:-

Where, P= Loan amount = $67,546.70

r = Periodic Interest rate = 0.08

n= no of periods

m = no o time lapsed

Outstanding Balance = $67,546.70/2 = $ 33,773.35

4.53132844455 = 10.0626568891 - (1.08)^m

(1.08)^m = 5.5313284446

Taking log both sides:

m log(1.08) = log(5.5313284446)

m(0.03342376) = 0.74282945

m = 22.22

So, it will take 22.22 years to make balance to half.

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