Accounting Problem: Securing a Permanent Position as an Accountant (Math Problem Sample)

Question
After completing your Bachelor of Business (Accounting) degree, suppose you secure a permanent position as an accountant. You drafted a financial plan to retire in 30 years from now. So, you are thinking about creating a fund that will allow you to receive $40,000 at the end of each year for 25 years after your retirement. The interest rates are expected to be 2.25% per annum during the 30year pre- retirement period and 1.75% during the retirement period.
Required:
* a) To provide the 25- year, $40,000 a year annuity, calculate how much should be in the fund account when you retire in 30 years.
* b) How much will you need today as a single amount to provide the fund calculated in part (a) if you earn 2.35% per year during the 30 years preceding your retirement?c) What effect would a change (increase/decrease) in the interest rates, both during and prior to retirement, have on the values calculated in parts (a) and (b)? Explain why.
* d) (Using different interest rates) Assume that the interest in the pre-retirement period is 1.65% and 2.15% in the post-retirement period. To fund the 25- year stream of $40,000 annual annuity payments, how much do you need to deposit annually? (Deposits are made at the end-of-year for 30 years).
 
Suppose you are planning for a 20-year mortgage to buy a residential property in Auckland. The property value is $950,000. You have got a pre-approval for 80% of the property value. The interest rate on the mortgage is 3.12% per annum, and the annual mortgage is to be paid at the end of each year.