Writing Recurrence Relations
State the starting value, t0, of the sequence 20, 19, 18, 17, .
t0=20
An investment of $5000 is made that pays interest of 4% per annum. How much interest does the investment pay each year?
$200
What am I?
- I start by investing my money into a savings account at the bank, where I gain interest.
I then produce a series of equal payments made at regular intervals to the original investor.
You might receive me as fixed income during retirement.
My payments can be monthly, quarterly, or yearly.
Annuity
Who am I?
I reduce the value of an asset by the same fixed amount every year.
My depreciation expense does not change over time.
I’m simple to calculate and often used for straight-line depreciation.
I assume the asset loses value evenly throughout its useful life.
Flat rate depreciation
What is Ms Robinson's favourite colour?
Green
Find the t5 from the sequence: 8, 12, 16, 20, ...
36
The following recurrence relation can be used to model a simple-interest investment. V0 = 8000, Vn+1 = Vn + 400.
When will the investment reach $12 000 in value?
10 years
What am I?
I’m a type of loan where the interest is calculated on the outstanding balance, not the original loan amount.
With every repayment, the principal I’m based on gets smaller.
My repayments start higher and reduce over time if payments stay constant.
I’m commonly used in mortgages and car loans.
Reducing Balance Loan
Who am I?
I charge more depreciation expense in the early years and less in later years.
I calculate depreciation as a fixed percentage of the asset’s previous value each year.
My value decreases by a smaller amount every year because the base keeps shrinking.
I reflect accelerated loss in value, common for vehicles and technology assets.
Reducing balance depreciation
Who is my all time favourite football player?
- Matthew Richardson OR
- Jake "the Push up" King
Jake "the Push up" King
Write down the first five terms of the sequence defined by the following recurrence relation:
P0 = 52, Pn+1 = Pn + 12
52, 64, 76, 88, 100
The following recurrence relation is used to model balance-reducing depreciation on an asset. V0 = 40 000, Vn+1 = 0.9Vn
State the annual percentage depreciation of the asset.
10%
I grow your money by earning interest on both your initial investment and the interest previously earned.
My growth accelerates over time, as no withdrawals are made
I can be described as “interest on interest.”
The longer you stay invested with me, the more your investment compounds.
Compound Interest Savings/Investment
Who am I?
I calculate depreciation based on how much an asset is used or produced.
My expense varies depending on activity level, like hours worked or units made.
I match the expense to the asset’s actual usage rather than time.
I’m useful when wear and tear depends on how much the asset is used.
Unit Cost depreciation
Which of these is false?
1. I went to university with the Army.
2. I worked at company that made and produced make up before teaching.
3. I can play the guitar.
FALSE - I can play the guitar (drums & french horn)
Rewrite the following recursion relation in symbolic form, where Vn represents the value after n applications of the rule.
The starting value is 3, and the rule is ‘add 7 to the current term and repeat the process’
V0 = 3, Vn+1 = Vn + 7
Simon invests $80 000 with a bank. He will be paid interest at the rate of 6% per year, compounding monthly.
Write a recurrence relation to model Simon’s investment.
V0 = 80 000. Vn+1 = 1.005Vn
When using finance solver.
PV = -ve
FV = +ve
Pmt = -ve
Money is invested with the bank, and is ongoing payments are also added whilst interest is accrued. I'm often used for superannuation accounts.
Annuity Investment
You all know that Ms Robinson plays netball. But did she deliberately break someone's nose doing this in her teenage years?
No, it was accidental haha
State the term name for the term that has a value of 44.
T0 = 20, Tn+1 = Tn + 3
T8 = 44.
The following recurrence relation can be used to model a compound-interest investment:
V0 = 12 000, Vn+1 = 1.08Vn, where Vn is the value of the investment after n years.
Use the rule to find the value of the investment after 4 years, giving your answer to the nearest dollar
V4 = 1.084 × 12 000 = $16 326.
What am I?
I require you to pay only the interest on the loan for a set period.
During that period, the principal remains unchanged.
You won't have enough money to finance your project so you will need to borrow from the bank.
Interest Only Loan
You all know that I have a dog called Abby.
She is a mixed breed.
She is a Staffordshire Bull Terrier crossed with what breed starting with B
Basenji