Compound Interest and Saving
What is compound interest used for in financial modelling?
To plan for future savings by calculating how money grows with interest over time.
A series of regular payments or deposits made over time.
What is an annuity?
What types of savings plans might be investigated?
Superannuation and long-term deposits.
A loan where interest is calculated on the remaining balance after each payment.
What is a reducing-balance loan?
What are two common types of loan interest rates?
Fixed and variable rates.
What are the four key variables in a compound interest calculation?
Future Value (FV), Present Value (PV), number of periods (n), and interest rate (I).
What is a future-value annuity?
The value of a series of regular payments at a future date, including compound interest.
What are two factors that can erode investment returns?
Taxation and inflation.
A loan where only interest is paid during the term, and the principal is repaid later (often via a sinking fund).
What is an interest-only loan?
A rate that includes interest, fees, and compounding effects to show the true cost of a loan.
What is a comparison rate?
How can compound interest models be improved to be more realistic?
By including regular deposits (annuities), fees, tax, and inflation effects.
What happens when the annuity model is reversed?
A lump sum can be used to provide a regular income (e.g., a pension).
How can different investment options be compared fairly?
By converting them to an equivalent annualised (effective) interest rate.
Increase payment frequency or amount, shorten the loan term, or make a lump-sum repayment.
Name two ways to reduce the total interest paid on a loan.
Why is the nominal rate not always what’s really paid?
It doesn’t include fees or account for compounding effects.
Compare Simple and Compound Interest
Simple Interest - always calculated on the original principal. Interest remains the same, regardless of the balance.
Compound Interest - calculated on the balance. Interest changes in line with the current balance (increases over time with the increasing balance for savings accounts and reduces over time with loans/mortgages)
What variables affect the future value of an annuity?
Payment amount, interest rate, and number of periods.
Why are effective interest rates important in advertisements?
They allow for fair comparisons between investment options with different compounding.
What does a sinking fund do?
Accumulates money to repay the principal of an interest-only loan.
What must be added to calculate a comparison rate when fees are involved?
One-off setup fees (application/administrative fees) added to PV and ongoing fees added to each payment.
Why might results from compound interest models not always be realistic?
Because they rely on assumptions like constant interest rates and no unexpected fees.
How does changing compounding periods affect annuity results?
More frequent compounding increases total interest earned or paid.
What are some charges that reduce returns on investments?
Bank and government fees, administration costs, and taxes
Why do early loan payments mostly cover interest?
Because interest is calculated on a larger principal at the start of the loan.
Why should borrowers compare more than just the interest rate?
Because fees, charges, and repayment frequency also affect total cost.