Question

Time value of money You are giving personal financial planning advice to your parents. Both of your parents have worked for Air New Zealand for 15 years. They have savings of $100,000 invested in Air New Zealand’s ordinary shares. They expect to be able to earn 6% compounded monthly on any investments or savings. Your parents wish to retire in 20 years. In retirement, they desire to have $5000 of monthly income for 25 years. At this point, they expect to die (or have you take care of them). Due to their great loyalty to Air New Zealand, they wish to invest their savings in Air New Zealand ordinary shares.

a. Draw a timeline showing your parents' financial plan.

b. How much will your parents have to save by May 2039, when they retire, so that they can get their desired monthly income from then on?

c. Find the present value (today) of the amount they will have to save by retirement (the amount you calculated in (b)).

d. What monthly savings will they need to make from now until retirement in order to save the amount they need to fund their retirement (the future amount you calculated in (b))?

Answer 1

b. Total accumulation at end yr. 20 / Start yr.21, from now, t=0

is the Present value of

Pmt.= monthly pmt., $ 5000

earning at an interest rate of r= 6% p.a. ie.6%/12=0.5% or 0.005 p.m.

for n=25*12=300 months

so, using the formula to find present value of ordinary annuity,

PVOA=Pmt.*(1-(1+r)^-n)/r

& plugging-in the above values.

PVOA=5000*(1-1.005^-300)/0.005=

776034.32

so, the answer for b. is

Amount your parents will have to save by May 2039, when they retire, so that they can get their desired monthly income from then on= $ 776034.32

c. The present value (today at t=0) of the amount they will have to save by retirement (the amount calculated in (b))=

Using the formula to find PV of a single sum in future, ie.

PV=FV/(1+r)^n

where FV= the accumulation needed at end yr. 20(as calculated above), ie,776034.32

r= 0.5% or 0.005 p.m

n= 20 yrs. *12= 240 mths.

so ,776034.32/1.005^240=

234437

d. Monthly savings they will need to make from now until retirement in order to save the amount they need to fund their retirement (the future amount you calculated in (b)):

Given that they already have savings of $100,000 invested in Air New Zealand’s ordinary shares & they expect to earn 6% compounded monthly on any investments or savings

so, the PV of balance to be saved, to meet the requirement in b.

234437-100000= 134437

$ 134437 is the PV of ordinary monthly annuity , Pmt.

for n= 20*12=240 months

at r= 0.5% or 0.005 p.m

so, again using the formula to find present value of ordinary annuity,

PVOA=Pmt.*(1-(1+r)^-n)/r

& plugging-in the above values.

134437=Pmt*(1-1.005^-240)/0.005

& solving for pmt., we get the further monthly amt. to be saved as ,

134437/((1-1.005^-240)/0.005))=

963.15

If they are going to make immediate payment

then we need to find the pV of annuity due , with the 1st monthly pmt. Being made now, at time, t=0

so, using the formula to find present value of annuity due(beginning of period annuity)

PVOA=Pmt.*(1-(1+r)^-n)/r*(1+r)

& plugging-in the above values.

134437=Pmt*(1-1.005^-240)/0.005*1.005

pmt.=134437/((1-1.005^-240)/0.005*1.005)=

958.36