Question

The Mendez family is considering a mortgage loan of $350,000 at an annual interest rate of 6.55%.

(a) How much greater is their mortgage payment if the term is 20 years rather than 30 years?


(b) How much less is the amount of interest paid over the life of the 20-year loan than over the life of the 30-year loan?

Answer 1

As provided in the question, the question is solved in easy way step by step. As nothing specified , 1st part is solved and steps to calcualte given for 2nd part.

Calculation of Mortgage payment for 20 years,

We first need calculate Annual Payment with Principal Amount = $3,50,000

Interest = 6.55%

Years = 20 years

Annual Payment using Excel Formula =PMT(Interest Rate, Years, -Principal Amount,0,0)

Annual Payment = $ 31,890

where principal = 8,966 (using excel formual (=ppmt(interest rate,1,years,-principal)

and, therefore, interest = 22,925

So, the 20years payment = 31,890 *20 = 6,37,800

After 30 years

Interest = 6.55%

Years = 30 years

Annual Payment using Excel Formula =PMT(Interest Rate, Years, -Principal Amount,0,0)

Annual Payment = $ 26,941

where principal for the first year= 4016 (using excel formual (=ppmt(interest rate,1,years,-principal)

and, therefore, interest for the first year = 22925

So, the 30years payment = 26,941*30 = 8,08,230

a) How much greater is their mortgage payment if the term is 20 years rather than 30 years? = Payment after 30 years - payment after 20 years = 8,08,230 - 6,37,800 = $1,70,430

b)using the excel formula stated above , interest for 20 and 30 years can be calculated and the difference of interest can be easily calculated.