Question

William has to make rental payments of $1,000 at the start of every month, throughout the four-year duration of his university course. His university fees are $4,000 to be paid at the start of each year. He 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 he keeps the part-time job for the next four years. How much money, in present value terms, can he withdraw each month for the next four years?

	A.	$144
	B.	$126
	C.	$55
	D.	$177

Answer 1

ANSWER

The present value of an annuity due (PV) for $1000 & $4000

PV = {C× [1-(1+r)^-n]/r}×(1+r)}

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)

The present value of an ordinary annuity (PV) of $1500

PV = C× [1-(1+r)^-n]/r

PV = Present value

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)

Difference of 2&1 = 6017.95

The present value of an ordinary annuity (PV).

PV = C× [1-(1+r)^-n]/r

PV = Present value

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

NEAR BY ANSWER IS OPTION (A)=$144

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