Question

Lionel purchased a house for $475,000. He made a downpayment of 25.00% of the value of the house and received a mortgage for the rest of the amount at 5.82% compounded semi-annually amortized over 20 years. The interest rate was fixed for a 4 year period.

a. Calculate the monthly payment amount.

b. Calculate the principal balance at the end of the 4 year term

c. Calculate the monthly payment amount if the mortgage was renewed for another 4 years at 3.62% compounded semi-annually?

Answer 1

Solution :-

Semiannual Rate = 5.82% / 2 = 2.91%

Now Monthly Rate = ( 1 + 0.0291 )^1/6 - 1 = 0.0047922 = 0.479%

Purchase Price = $475,000

Down Payment = 25% * $475,000 = $118,750

Amount financed = $475,000 - $118,750 = $356,250

In 20 Years , Total monthly Payments = 20 * 12 = 240

(a) Monthly Payment = $356,250 / PVAF ( 0.479% , 240 ) =

= $356,250 / 142.4255

= $2,501.31

(b) At the end of 4 year term , total = 192

Now Principal Balance = $2,501.31 * PVAF ( 0.479% , 192 )Payment remaining = 16 * 12

= $2,501.31 * 125.338

= $313,508.85

(c) Semiannual Rate = 3.62% / 2 = 1.81%

Now Monthly Rate = ( 1 + 0.0181 )^1/6 - 1 = 0.002994 = 0.2994%

New monthly Payments = 16 * 12 = 192

New monthly = $313,508.85 / PVAF ( 0.2994% , 192 )

= $313,508.85 / 145.865

= $2,149.31

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