Question

You have the option to take out a 30-year mortgage that has an APR of 4.9% or a 20-year mortgage that has an APR of 4.15%. When answering the following questions, remember to base your mortgage payments on the amount you need to borrow rather than the entire purchase price.

30-year mortgage
If you take out a 30-year mortgage with an APR of 4.9%, what will your monthly payment be? (Round your answer to the nearest cent.)

$

If you make the payment you just calculated every month for 30 years, how much will you pay altogether?

$

What dollar amount of your total 30-year mortgage payments go to interest?

Hint: The dollar amount of your interest is the difference between your total payments and the amount you borrowed.

$

What percentage of your total 30-year mortgage payments go to interest? (Round your percentage to one decimal place.)

%

20-year mortgage
If you take out a 20-year mortgage with an APR of 4.15%, what will your monthly payment be? (Round your answer to the nearest cent.)

$

If you make the payment you just calculated every month for 20 years, how much will you pay altogether?

$

What dollar amount of your total 20-year mortgage payments go to interest?

Hint: The dollar amount of your interest is the difference between your total payments and the amount you borrowed.

$

What percentage of your total 20-year mortgage payments go to interest? (Round your percentage to one decimal place.)

%

30-year vs 20-year mortgage
How much money will you save altogether by taking out a 20-year mortgage rather than a 30-year mortgage?

Answer 1

NOTE:

All inclusive Loan requirement taken as $ 100,000

EMI Formula = P * r * (1+r)^n / [(1+r)^n)-1] , where

P is the Loan amount i.e. $ 100,000

r is the monthly APR i.e APR/12.So for 30 year it is 4.9%/12 or 0.41% and for 20 year it is 4.15%/12 or 0.35%

n is the period of loan in months i.e for 30 year it will be 12*30 or 360 and for 20 years it will be 20*12 or 240

Basis the above all calculations are done below.

30 YEAR MORTGAGE:

EMI = 100,000 * 0.41% * (1+0.41%)^360 / [(1+0.41%)^360)-1] (data refer to NOTE segment above)

EMI = 530.73

With the above rate total payment in 360 months or 30 years will amount to

530.73 * 360 = 191061.62

Interest amount = Total Payments - Borrowings = 191061.62 - 100000 = 91061.62

Interest component in perecentage terms will be :

Interest / Total Payment = 92376.68 / 192376.68 = 47.7%

20 YEAR MORTGAGE:

EMI = 100,000 * 0.35% * (1+0.35%)^240 / [(1+0.35%)^240)-1] (data refer to NOTE segment above)

EMI = 613.91

With the above rate total payment in 240 months or 20 years will amount to

613.91 * 240 = 147339.23

Interest amount = Total Payments - Borrowings = 147339.23 - 100000 = 47339.23

Interest component in perecentage terms will be :

Interest / Total Payment = 47339.23 / 147339.23 = 32.1%

30-year vs 20-year mortgage

Savings = Total Payment under 30 year mortgage - Total Payment under 20 year mortgage =  191061.62 - 147339.23 = 43722.39