How does recursion model a compound interest investment that grows each period?
Model compound interest with a recurrence relation, convert nominal annual rates to the period rate, and find balances and effective rates.
How to model a compound interest investment with a recurrence relation, convert a nominal annual rate to the compounding-period rate, find any balance, and compare effective annual rates.
Reviewed by: AI editorial process; not yet individually human-reviewed
Have a quick question? Jump to the Q&A page
Jump to a section
What this dot point is asking
You must set up the recurrence, get the period interest rate right when compounding is more often than yearly, find balances, and compare investments using the effective annual rate.
The recurrence model
Compound interest pays interest on the balance, so the balance grows geometrically.
The recurrence form shows the period-by-period growth; the explicit form jumps to any balance.
Getting the period rate right
When interest compounds more often than annually, you must convert the nominal annual rate to a rate per period and count periods accordingly.
Effective annual rate
To compare investments with different compounding frequencies fairly, convert each to its effective annual rate: the single yearly rate that gives the same growth.
Reading the question carefully
The two traps are the period rate and the period count. Always identify how often interest compounds, divide the annual rate by that number, and multiply the years by that number to get . A yearly rate used directly with monthly compounding overstates the growth badly.