Question

5 years ago, Jimmie borrowed $281,900 to purchase a house in Sandy Lake. At the time, the quoted rate on the mortgage was 6 percent, the amortization period was 25 years, the term was 5 years, and the payments were made monthly. Now that the term of the mortgage is complete, Jimmie must renegotiate his mortgage. If the current market rate for mortgages is 7 percent.

What is Jimmie’s new monthly payment? (Round effective monthly rate to 6 decimal places, e.g. 25.125412% and final answer to 2 decimal places, e.g. 125.12. Do not round your intermediate calculations.)

Answer 1

Firstly, Calculating the Outstanding Loan Balance after 5 years at the end of the term:-

$Outstanding Balance = P*\frac{[(1+r)^{n}-(1+r)^{m}]}{(1+r)^{n}-1}$

Where, P = Loan MAount = $281,900

r = Perodic iInterest rate = 6%/12 = 0.5%

n= no of periods of loan = 25 yrs*12 =300

m = no of payments already made = 5yrs*12 =60

$Outstanding Balance = 281,900*\frac{[(1+0.005)^{300}-(1+0.005)^{60}]}{(1+0.005)^{300}-1}$

$Outstanding Balance = 281,900*\frac{[4.46496981216-1.34885015255]}{4.46496981216-1}$

Outstanding Balnace at the end year 5 year = $253,518.55

Now, the Market rate of mortgage = 7%

Calculating the new monthly loan Payment:-

Monthly Payment = P*r* (1+r)" (1+r)" - 1

Where, P = Loan MAount = $253,518.55

r = Perodic iInterest rate = 7%/12 = 0.583333%

n= no of periods of loan = 20 yrs*12 =240

$Monthly Payment= 253,518.55*0.00583333*\frac{(1+0.00583333)^{240}}{(1+0.00583333)^{240}-1}$

$Monthly Payment= 253,518.55*0.00583333*\frac{4.03873563673}{4.03873563673-1}$

Monthly Payments = $1965.53

So, New monthly Payment is $1965.53

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