Question

Peter intends to retire in 25 years time. he decides to save 500 at the start of each month until he retires. The pension fund is offering him a rate of 5.2% AER.

(A) (i) Find the rate of interest compounded monthly that would be equivalent to an AER of 5.2%, correct to 6 significant figures.

(ii) What lump sum will peter receive on his retirement?

(B) Peter uses his retirement fund to purchase an annuity at 4.2% AER. This will give him a repayment at the start of each month for the next 25 years. What will his monthly payment be?

Answer 1

Part A)

i)

AER= 5.20%

Rate of interest compounded month (r):

AER = (1+r/)^m -1

0.052 +1 = (1+r/12)^12

r= 0.004233362 x 12

r= 5.08%

ii)

we have:

pmt = 500

n= 25x12 = 300

R= 0.0508/12 = 0.004233

Future value for an annuity due

FV = Pmt x FVIFA(n, r) x (1+r)

FV = 500 x FVIFA(300, 0.004233) x (1+0.004233)

     = 500 x 602.6379615 x 1.004233

     = $302,594.46

Part B

Monthly rate R= (1+AER)^(1/m) -1

                         = (1+0.042)^(1/12) -1

                         = 0.00343438

PV = $302,594.46

N = 25x12 = 300

Pmt = PV /( PVIFA(N,R) x (1+R))

        = $302,594.46 / (PVIFA(300, 0.00343438) x (1+ 0.00343438)

        = 302594.46 / (187.07149 x 1.00343438)

        = $1612

Therefore, monthly withdrawal amount would be $1612.