Question

Karen has to make rental payments of $1000 at the start of every month, throughout the four-year duration of her university course. Her university fees are $4000 to be paid at the start of each year. She earns $1500 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? I have seen different answers from multiple people (eg: 146.13 and 157.83), and am not sure which is right or if none of them are right. Please help me. Thank you :)

Answer 1

Interest rate per year = 8% pa

Interest rate per Month = 0.667%

Rental Payment of $1000 are to be paid at the start of every month for 4 years.

Total Number of Months = 4*12= 48 months

Present value of Annuity due =

A = Monthly withdraw at the begin = $1000

i = interest rate per Month = 0.667% or 0.00667

n = total period = 48 months

hence PV of rental payment =

=>PV of rental payment= $41234.99

Similarly,

PV of the annual university fees payment of $4000 at the start of each year =

A = Annual withdraw at the begin of each year = $4000

i = interest rate per annum = 8% or 0.08

n = total period = 4 yr

PV of the annual university fees payment=

=>PV of the annual university fees payment = $14308.39

Present value of ordinary annuity(Payment at end) =

A = month end saving= $1500

i = interest rate per Month = 0.667% or 0.00667

n = total period = 48 months

Present value of Monthly saving =

=>Present value of Monthly saving= $61442.87.

PV of monthly saving = PV of rent payment+ PV of Fees payment+ PV of monthly withdraw

=>$61442.87=$41234.99+$14308.39+PV of monthly withdraw

=>PV of monthly withdraw = $5899.49

Let the Monthly withdraw be ''A'' at the end of each month.

PV of monthly withdraw =

PV of monthly withdraw = $5899.49

i = interest rate per Month = 0.667% or 0.00667

n = total period = 48 months

hence

=>A = $144.02 OR $144.

She withdraw each month for the next four years = $144.02 or $144. [ Final Answer]

Note- No intermediate calculations have been Rounded off. Only the final answer has been rounded off.