Recursion

Question 1:

Mrs Jackson opened a fixed deposit account in which she invested $525 at 3.25% p.a. simple interest. Mrs Jackson planned to leave the money there for a full 5 years.

a. Set up a recurrence relation to find the value of the investment after years.

Question 1:

b. Use the recurrence relation from part (a) to find the value of the investment at the end of each year and hence state the value of the investment at the end of the 5-year period.

Please label answers as

1: _____, _____, 2: _____, _____, 3: _____, _____, 4: _____, _____,

5: _____, _____

Answer: $________

Question 2:

Approximately how long would it take for Sarah to save up for a $5000 for a holiday, if she has $3500 now and elects to invest her money at 12%p.a, interested credited monthly?

n = _______________

Question 3:

The cost of a brand-new plus TV was $23999. It depreciates at a rate of 45% p.a.

a. Calculate the total depreciation after 2 years

Total depreciation = ______________

Question 3:

b. Generate a depreciation schedule to establish how long it will take for the brand-new plus TV to be worthless, if the brand-new plus TV is considered worthless when less than $100 in value.

Please label answers as:

0: __________, 1: __________ 2:__________, 3:__________ 4:__________, 5:__________, 6: __________

Question 4:

After depositing some money in a savings account earnings 4.5% p.a. simple interest, Michelle was told that she had accrued $496 in interest after 2 years. What amount had she originally invested?

The amount originally invested = $ ____________

Question 5:

Jo’s sister in law Grace is about to retire and is wondering what to do with her superannuation money.

One option is to invest her $625 000 in an annuity paying 4.5%p.a. compounding monthly.

a. How much would she receive per month if the annuity is for 20 years?

She will receive $___________ per month

Question 5:

b. If she decided that she wanted to receive $4000 per month, how many fewer payments would she receive from the annuity?

She will receive __________ fewer payments

Question 5:

c. Another annuity company claims that their annuit product would give her $4250 per month for twenty years for the $625 00 investment. What interest rate, correct to decimal place, would give this return?

The correct interest rate is: _____________

Question 5

d. What is the difference between an annuity and a perpetuity?