Financial Plan to Retire in 30 years (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.
* Calculate the annual mortgage payment on the loan
Construct a mortgage amortisation table showing the loan balance at the beginning of each period, annual repayment amount, interest payment, the amortisation of the loan and the loan balance for each year.
Answer
Step 1 Present value concept in retirement:
Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved, then please specify the question number or post only that question.
The present value concept is an important time value of money concept that determines the value of future funds at the present period. The present value of funds can determine with the help of the total period of retirement and savings and interest period. The annuity here is the series of payments and receivables. The present value concept provides the fund requirement for retirement planning, savings, and investment.
Step 2 Part a) Required fund for retirement annuities:
The given information:
Desired annuity for next 25 years: $40,000, Interest rate: 1.75%
value of annuities at 30th year=====Annuity value[1−(1+interest rate)−yearsinterest rate]40,000[1−(1.0175)−250.0175]40,000[0.35190368430.0175]40,000[20.1087819611]$804,351.278444value of annuities at 30th year=Annuity value1-(1+interest rate)-yearsinterest rate=40,0001-(1.0175)-250.0175=40,0000.35190368430.0175=40,000[20.1087819611]=$804,351.278444
Hence, the funds required in 30 years will be $804,351.278444
Step 3 Part b) Present value of required funds:
The required funds in 30 years will be $804,351.278444, interest rate: 2.35%, time: 30 years.
Present value of fun