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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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Noah invests $22,804 in a term deposit, which pays interest at 3% p.a.

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

Suppose interest compounds yearly. Find (i) the rate per year and (ii) the multiplier this corresponds to, from the annual rate of 3%

Rate per year Multiplier

Under yearly compounding, what does one step of the index $n$ count?

Year

Day

Fortnight

(d)2 marks

Suppose interest compounds quarterly. Find (i) the rate per quarter and (ii) the multiplier this corresponds to, from the annual rate of 3%

Rate per quarter Multiplier

(e)1 mark

Under quarterly compounding, what does one step of the index $n$ count?

Week

Quarter

Year