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Write a recurrence relation for a loan or investment with a given compounding period

Question 1 of 8

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A home loan of $524,327, at 7.2% p.a., is set up by Priya

Suppose interest can compound at different frequencies. Model the balance below for each compounding arrangement in turn

The quoted annual interest rate is nominal, convertible at the stated compounding frequency. It is not an effective annual rate

(a)1 mark

What is the starting value $V_0$ of the balance, in dollars?

Starting value ($)

(b)2 marks

If interest compounds yearly, convert the 7.2% p.a. rate to a rate per year, then write the multiplier

Rate per year Multiplier

If interest compounds yearly, what does $n$ count in the recurrence relation?

Year

Week

Fortnight

(d)2 marks

If interest compounds monthly, convert the 7.2% p.a. rate to a rate per month, then write the multiplier

Rate per month Multiplier

(e)1 mark

If interest compounds monthly, what does $n$ count in the recurrence relation?

Year

Quarter

Month