Question 1Paper 1 style
A loan is modelled by , , where is the balance in dollars at the beginning of the th month. Which one of the following describes the loan?
QCE General Maths loans, annuities and perpetuities
Every model in this part of the course is a recurrence: the amount is multiplied by one plus the interest rate per period, then a payment is subtracted (a loan or pension) or added (a regular investment). The formulas give the same answers in one step.
| Paper 1 | Short response and multiple choice, 30% |
|---|---|
| Paper 2 | Short response, 20% |
| Each paper | 5 minutes perusal, 90 minutes working |
| Allowed | A scientific calculator and the formula book |
Which formula
- Compound interest with no payments: A = P(1 + i) to the power n.
- A loan or a pension paid from a lump sum: the present value of an ordinary annuity.
- Regular deposits building a balance: the future value of an ordinary annuity.
Match the rate to the period
The interest rate i in every formula is the rate per compounding period: an annual rate of 6% compounding monthly is 0.5% a month, and n counts months.
Try 2 questions
Question 2Paper 1 style
A sports club wants to award a $4000 prize at the end of every year, forever. Its fund earns 5% per annum, compounding annually. What amount must be invested in the fund now?
Next step
Questions people ask
What is the effective annual rate?
The interest a year actually adds once it compounds more often than yearly: (1 + i) to the power k, minus 1, with i the rate per period and k the periods in a year.
What is an ordinary annuity?
One where each payment is made at the end of a period, after that period's interest is calculated.