What's the word?
It's not compound interest.
What is simple interest?
The general form of a reducing balance loan recurrence relation.
What is An+1 = rAn-R?
Complete the first payment row below.
Payment Payment Interest Principal Balance
number reduction
0 $0.00 $0.00 $0.00 $1500.00
1 $382.06 $11.25 $370.81
$1129.19
A person invests $5000 in a financial institution at 6%p.a. compounded annually. Calculate the balance on this account at the end of 4 years.
$6312.39
How you calculate the future value for compound interest.
What is A=P(1+i)n?
The starting amount of money for a loan or investment.
What is the principal?
Identify the opening balance for the second quarter.
Quarter Opening Investment Deposit Closing
balance gain balance
1 $5000.00 $600.00 $210.00 $5810.00
$5810
Calculate the closing balance after two payments on the loan modelled below.
Jenny borrows $6500 for an overseas trip and takes a personal loan at an interest rate of 11.5%p.a. compounded fortnightly, with fortnightly repayments of $98.72 over 3 years.
$6359.75
How you could calculate successive values in a reducing balance loan.
An+1=rAn-R
A form of compound interest investment into which regular and equal payments are made periodically for a fixed period of time, or a single sum investment from which regular and equal payments are received.
What is an annuity?
A person invests $5000 in a financial institution at 6% per annum compounded annually. Using A0 to represent the initial investment, write this scenario as a recurrence relation.
A0 = 5000, An+1=1.06An
Complete the first payment row below.
Payment Payment Interest Principal Balance
number reduction
0 $0.00 $0.00 $0.00 $2400.00
1 $489.64 $471.64 $1928.36
$18
$400 is invested at the end of every 6 months for 12 years at 12%p.a. with interest compounded six monthly. Calculate the future value of the annuity on maturity.
$20326.23
How you compare interest rates to make the best financial decision.
Effective interest rate formula
ieff.=(1+i/n)n-1
The actual percentage return per year on an investment or loan.
What is an effective interest rate?
Bob borrows $3500 at a rate of 6.5%p.a. with interest compounded monthly, which is to be paid back with monthly instalments of $711.42. Write a recurrence relation to describe this situation.
A0=3500, An+1=1.00542An-711.42
$2400 is borrowed at 9%p.a. and is paid back with monthly instalments of $489.64. Calculate the closing balance of payment two.
Payment Payment Interest Principal Balance
number reduction
0 $0.00 $0.00 $0.00 $2400.00
1 $489.64 $471.64 $1928.36
2 $489.64
Interest charged is $14.46 so
principal reduction is $475.18 so
balance of loan is $1453.18
Patrick was offered an investment rate of 4.97%p.a. compounding daily or 5%p.a. compounding monthly. Which should he choose?
How you calculate the future value of a compounding interest loan where regular and equal repayments are made.
Annuity formula with the negative n variable
A = M(1-(1+i)-n/i)
A table for repeated calculations, typically seen in reducing balance loans.
What is amortisation?
An investment made at 8.4%p.a. for 4 years with interest compounded quarterly has the following activity in it's first quarter. Write a recurrence relation to represent this situation.
Quarter Opening Investment Regular Closing
balance gain deposit balance
1 $1200.00 $25.20 $110.00 $1335.20
A0=1200, An+1=1.021An+110
Determine the closing balance after 3 payments have been made.
An+1=1.0075An-600.35, A0=45000
Payment Payment Interest Principal Closing
number reduction balance
0 $0.00 $0.00 $0.00 $45000
1
2
3
$44205.52
A college alumni decides to set up a scholarship fund for a gifted musician at his old college. He invests $80000 and wants to have regular six-monthly payments of $3000 generated. Determine the per annum interest rate he needs to negotiate with the bank to make this happen.
7.5%p.a.
The one special relationship you do need to actually remember for perpetuities to be able to create the following equations.
Triangle A M i
A=M/i
M=Axi
i=M/A