Question

Karen has to make rental payments of $1,000 at the start of every month, throughout the four year duration of her university course. Her University fees are $4,000 to be paid at the start of each year. She earns $1,500 per month (paid at the end of each month) from a part time job.

Assume an interest rate of 8% p.a. and that she keeps the part time job for the next four years. How much money, in present value terms, can she withdraw each month for the next four years?

Answer 1

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1. Formula: The present value of an annuity due (PV) for $1000 & $4000

PV = {C× [1-(1+r)^-n]/r}×(1+r)}

PV = Present value (The cumulative amount available at Present).

C= Periodic cash flow. 1000/4000

r =effective interest rate for the period. (1.08^(1/12))-1 = 0.6434%/8%

n = number of periods. 48/4

PV = {1000× [1-(1+0.006434)^-48]/0.006434}×(1+0.006434)}+{4000× [1-(1+0.08)^-4]/r}×(1+0.08)}

PV = 55,755.96 (1)

2. Formula: The present value of an ordinary annuity (PV) of $1500

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)

C= Periodic cash flow.

r =effective interest rate for the period.

n = number of periods.

PV = 1500× [1-(1+0.006434)^-48]/0.006434

PV = 61,773.91 (2)

3. Difference of 2&1 = 6017.95

Formula: The present value of an ordinary annuity (PV).

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)

C= Periodic cash flow.

r =effective interest rate for the period.

n = number of periods.

6017.95 = C× [1-(1+0.006434)^-48]/0.006434

C = $146.13

The amount which Karen can withdraw =$146.13