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Assume that you take a 30-year mortgage for $800,000 at 9% p
Assume that you take a 30-year mortgage for $800,000 at 9% p.a. It is to be repaid monthly. from E to G please a. What is the monthly repayment amount? Assume the interest is compounded monthly b. How long does it take to pay off 40% of the principal (i.e. to have $480,000 outstanding)? c. What is the balance outstanding after four years? d. Four years after the mortgage starts, you are able to pay $400 more into your mortgage, what impact would this have on the remaining terms of your mortgage? e. If the interest rate increases to 9.6% after 4 years, what will be your new monthly repayment? f. Assume your parents would like to help you with the extra monthly payment due to the increase in the interest rate from 9% to 9.6%. What is the lump sum amount of money they need to give to you so that your monthly payment will remain the same as in part a? g. If at the end of year 4, the bank wishes to change your repayment from monthly to per fortnight, what is the APR the banks should offer so that you are indifferent between this new offer and the initial arrangement (i.e. 9% p.a. interest rate and monthly repayment)?
Expert Solution
e.
Loan amount = $800,000
Initial monthly rate = 9 / 12 = 0.75%
Number of months = 30 x 12 = 360
Monthly payment = PV x r / [1 - (1 + r)-n] = 800,000 x 0.0075 / [1 - (1 + 0.0075)-360] = $6,436.98
After 4 years, number of months remaining = (30 - 4) x 12 = 312
Balance remaining = P x [1 - (1 + r)-n] / r = 6,436.98 x [1 - (1 + 0.0075)-312] = $774,864.55
After the rates increase, new monthly rate = 9.6 / 12 = 0.8%
New payment = PV x r / [1 - (1 + r)-n] = 774,864.55 x 0.008 / [1 - (1 + 0.008)-312] = $6,761.74
f.
Difference in payments = 6,761.74 - 6,436.98 = $324.76
Lump sum = Difference in payments x number of remaining payments = 324.76 x 312 = $101,325.12
g.
With an APR of 9% compounded monthly, effective annual rate = (1 + 0.09/12)12
Fortnight is a period of 2 weeks. Number of fornights in a year = 52 / 2 = 26
Let r be the new APR
(1 + 0.09/12)12 = (1 + r/26)26
(1 + r/26) = 1.0034546
r/26 = 0.0034546
r = 0.08982 or 8.982% p.a with fortnightly repayment.
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