Question

MAN2 3000A%20May june%202017 %20MCQ9620Removedpdf Question 11 (answer all parts Nick has just turned 25 and considers joining the pension plan offered by his employer. If he joins the pension plan, Nick will need to pay annual contributions during his employment. The first contribution should be paid on his 26th birthday (i.e., in a year's time). Nick plans to retire on his 65 birthday (ie., in 40 years' time). when he would have to pay his last contribution to the pension plan. His life expectancy is 85 years. During his retirement (i.e., until his 85 birthday), Nick wants to receive £30,000 per year, starting from his 66 birthday. The interest rate that applies to the entire period is 5% per year. a) Find the present value (today) of the cash flows that Nick wants to receive from his 66th birthday until his 85h birthday. (10 marks) b) Find the amount that Nick has to contribute to the pension plan every year during his employment to finance the cash flows he wants to receive during his retirement. (10 marks) c) Nick finds the annual contribution he has to make very high and seeks financial advice. An advisor suggests to him to retire at the age of 70 instead of 65. If he follows this advice, find the annual contribution that Nick will have to make during his employment to finance the cash flows of £30,000 per year that he wants to receive during his retirement (i.e., from his 71 birthday until his 85h birthday). Explain why this is lower than the annual contribution calculated in b). (10 marks) d) Nick is also aware of the possibility that his life expectancy may increase to 90 years, and he is concerned that he will not receive any cash flow after the age of 85. If he decides to retire at the age of 70, how much will he need to contribute to the pension plan per year during his employment to receive £30,000 per year during his retirement until the age of. 90? (5 marks) (TOTAL 35 marks) PTO

Answer 1

a) First we will calculate present value at the end of 65th birthday

formula for present value of annuity is

PV- PV = P ×

Where PV is Present value of annuities

   P is value of annual payments

   r is interest rate

   n is number of periods

In the given question P= 30000, r = 0.05, n = 20

(1-(1 + 0.05) 20) 0.05 PV-30000 ×

(11-( 1.05)-") PV- 0.05

(1-0.3769) 0.05 PV-30000 ×

0.6231 0.05 PV-30000 ×

PV= 373,860

Now we will calculate present value as on today

Futurevalue Presentualue

373860 Presentvalue 10.05)40

Presentvale373860 7.04

Present value= 53,105.11

b) Formula for future value of annuities payable at the end of year is

$FV=P\left [ \frac{(1+r)^{n}-1}{r} \right ]$

P = FV

Where FV is Future value

   P is Periodic payment

   r is rate per period

n is number of periods

In the given question FV= 373,860 , r =0.05, n=40 and we need to find P

$P=373860\left [ \frac{0.05}{(1+0. 05)^{40}-1} \right ]$

$P=373860\left [ \frac{0.05}{7.04-1} \right ]$

$P=373860\left [ \frac{0.05}{6.04} \right ]$

P=3094.88

amount of contribution to pension required is 3094.88 every year

c) First we need to calculate present value on 70th birthday(n=15year)

$PV=30000\times \left ( \frac{(1-(1+0.05)^{-15})}{0.05}\right )$

$PV=30000\times \left ( \frac{(1-(0.481)}{0.05}\right )$

$PV=30000\times \left ( \frac{0.519}{0.05}\right )$

PV= 311,400

Now we need to calculate pension contribution to be made for 45 years

$P=311,400\left [ \frac{0.05}{(1+0. 05)^{45}-1} \right ]$

-31. P-31 1.400 |-一0.05 8.985-1

$P=311,400\left [ \frac{0.05}{7.985} \right ]$

P= 1949.91

Pension contribution to be made is 1949.91. this is less because number of year of contribution is 5 year more and retirement benefit period is 5 year less.

d)First we need to calculate present value on 70th birthday is he need pension till 90th birthday (n=20year)

(1-(1 + 0.05) 20) 0.05 PV-30000 ×

(1-(1,05) '") PV = 30000 × 0.05 (1-0.3769) PV 30000 × 0.05 30000 y (0.6231 PV- 373,860

Now we need to calculate pension contribution to be made for 45 years

$P=373860\left [ \frac{0.05}{(1+0. 05)^{45}-1} \right ]$

373860 0.05 7.985

P= 2,341

Amount need to be contributed to pension fund is 2341