Question

# Lionel purchased a house for \$475,000. He made a downpayment of 25.00% of the value of...

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?

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

#### Earn Coins

Coins can be redeemed for fabulous gifts.