Question

Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance. Thirty​-year mortgage for $250,000 at 3.54​%; remaining balance after 12 years.

Answer 1

Calculating the monthly payment interest is on the unpaid balance:-

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

Where, P = Loan Amount = $250,000

r = Periodic Interest rate = 3.54%/12 =0.295%

n= no of periods = 30yrs*12 = 360

Monthly Payment 250,000 * 0.00295 * (1 +0.00295) 300 (1 + 0.00295 360 – 1

$Monthly Payment = 250,000*0.00295*\frac{2.88763152295}{2.88763152295-1}$

Monthly Payment = $1,128.20

b), Calculating the remaining balance after 12 years:-

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

Where, P = Loan Amount = $250,000

r = Periodic Interest rate = 3.54%/12 =0.295%

n= no of periods = 30yrs*12 = 360

m = no of payments made = 12yrs*12 =144

$Outstanding Balance = 250,000*\frac{[(1+0.00295)^{360}-(1+0.00295)^{144}]}{(1+0.00295)^{360}-1}$

$Outstanding Balance = 250,000*\frac{[2.88763152295-1.52832849237]}{2.88763152295-1}$

Outstanding/Remaining Balance = $117,683.21

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