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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Mortgage A couple needs a mortgage of $ 300 , 000 . Their mortgage broker presents them with two options: a 3 0 - y e a r mortgage at 6 1 2 % interest or a 1 5 - y e a r mortgage at 5 3 4 % interest.

(a) Find the monthly payment on the 3 0 - y e a r mortgage and on the 1 5 - y e a r mortgage. Which mortgage has the larger monthly payment?

(b) Find the total amount to be paid over the life of each loan. Which mortgage has the lower total payment over its lifetime?

To determine

(a)

To find:

The monthly payment on the 30-year mortgage and on the 15-year mortgage.

The mortgage with larger monthly payment.

Explanation

Given:

A couple needs a mortgage of $300,000. Their mortgage broker presents them with two options: a 30-year mortgage at 612% interest or a 15-year mortgage at 534% interest.

Approach:

Installment buying formula,

R=iAp1(1+i)ni=Imn=m×t

Here,

R is the amount of monthly payment,

Ap is the present value of annuity,

i is the interest per time period,

I is the interest rate,

m is the no. of period,

t is the time-period in years and

n is the total number of installments.

Calculation:

Consider the values, Ap=$300,000, I1=612%, m=12 and t1=30.

i1=I1m=13/212×100=0.06512

n1=m×t1=30×12=360

Substitute 0.06512 for i1, 360 for n1 and 300, 000 for Ap in the formula given below:

R1=i1Ap1(1+i1)n1=0.06512×300,0001(1+0.06512)360=1625×(1+0.06512)360(1+0

To determine

(b)

To find:

The total amount to be paid over the life of each loan. The mortgage with the lower total payment over its lifetime

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