# Math Help - Theory questions

1. ## Theory questions

I have these questions, I'd appreciate any comment.

Citibank has just introduced a 40 year mortgage to the Australian market. Consider a $300,000 loan to be repaid with weekly repayments and an interest rate of J52= 8.00% p.a. a) Determine the size of the weekly repayment for a 30 year loan, and compare this with the size of the repayment for a 40 year loan. I got: 30 year loan, R=$ 507.6789
40 year loan, R= $481.2011 b) Determine the outstanding principal after 30 years of repayments on a 40 year loan. I just calculated the PV of the 520 remaining payments (2080 week-1560weeks= 520). I got$ 172,152.8282.

c) Explain why in (a) the relative decrease in payment size is much smaller than the relative increase in the duration in the loan?

Im not sure what to say here. Any suggestion?

d) The CEO of Aussie Home loans claimed that this means that a 40 year loan for $300,000 would cost a person over a million dollars by the time they had paid it back, and that "this is madness". Discuss wether his comment is correct or misleading? Explian why. I think that in term og absolute figures in deed the payment at the end would be more than a million dollars, but the CEO has forgotten the concet of the Time Value of Money. One million dollar in 40 years time wont be worth as much as one million dollars today, instead much more less. (Am I in the right direction?) Thanks guys, your help has been awesome and sorry for my ignorance with these matters!! Mauricio 2. Originally Posted by 10219929 I have these questions, I'd appreciate any comment. Citibank has just introduced a 40 year mortgage to the Australian market. Consider a$300,000 loan to be repaid with weekly repayments and an interest rate of J52= 8.00% p.a.

a) Determine the size of the weekly repayment for a 30 year loan, and compare this with the size of the repayment for a 40 year loan.

I got: 30 year loan, R= $507.6789 40 year loan, R=$ 481.2011

b) Determine the outstanding principal after 30 years of repayments on a 40 year loan.

I just calculated the PV of the 520 remaining payments (2080 week-1560weeks= 520). I got $172,152.8282. c) Explain why in (a) the relative decrease in payment size is much smaller than the relative increase in the duration in the loan? Im not sure what to say here. Any suggestion? d) The CEO of Aussie Home loans claimed that this means that a 40 year loan for$ 300,000 would cost a person over a million dollars by the time they had paid it back, and that "this is madness". Discuss wether his comment is correct or misleading? Explian why.

I think that in term og absolute figures in deed the payment at the end would be more than a million dollars, but the CEO has forgotten the concet of the Time Value of Money. One million dollar in 40 years time wont be worth as much as one million dollars today, instead much more less.

(Am I in the right direction?)

Thanks guys, your help has been awesome and sorry for my ignorance with these matters!!

Mauricio
Good job on what you've done. It checks out.

On (c): what follows compares the percentage increase in the payment on the 40 year loan to the percentage decrease in duration. (This is the opposite direction of the question, but the percentages work out better.)

Using the answer to (b), out of total payments after 30 years, only 17.48% went to pay down the principal. An increase in the payment from 481 to 507 would be an increase of 5.50%. This represents a percentage increase in payments to principal of 5.50/17.48 = 31.48%. To summarize, a 5.50% increase in total payment amount results in a 31.48% increase in payments to principal, which in turn results in a 25% decrease in duration as the loan is paid off faster.