Financial Assignment involving annuities

[Meercat92]

The Question is as follows;

An individual age 30 is planning to start investing in a personal pension. Her
aim is to have sufficient funds to provide a monthly pension of £1000 when
she retires at the age of 65, payable for 30 years. She is able to make bi-annual
contributions to the fund from her salary bonus. In order to facilitate planning,
she has found that current pension annuity interest rates are r12 = r % and
current savings rates are r4 = r %.
a) How much does she need to have in her pension pot in order to purchase
this annuity to provide her pension at 65?
b) How much will she have to set aside every six months in order to save
this amount?

r is given to be 5.71%

I'm struggling for ideas and don't know where to start
Anybody have any ideas?

 

[lippyka]

a) The amount she needs to have in her pension pot can be calculated by using the present value of an annuity formula. This formula states that: PV = A / (1 + r12)^30 where PV is the present value of the annuity, A is the amount of the annuity payments and r12 is the interest rate. In this case, A = 1000, r12 = 0.0571 and we want to find the present value of the annuity. Plugging in the numbers, we get PV = 1000 / (1 + 0.0571)^30 PV = £69,821.35 b) The amount she will have to set aside every six months in order to save this amount can be calculated by using the present value of a savings account formula. This formula states that: PV = A / (1 + r4)^30 where PV is the present value of the savings account, A is the amount of the regular payments and r4 is the interest rate. In this case, A = 69,821.35, r4 = 0.0571 and we want to find the present value of the savings account. Plugging in the numbers, we get PV = 69,821.35 / (1 + 0.0571)^30 PV = £2,919.80 Therefore, she will have to set aside £2,919.80 every six months in order to save the required amount.