Question

1. Don is planning for retirement. He has $25000 per year that he can invest 12500 semiannually to help fund his retirement. How much will the fund be worth in 14 years if he chooses a fund that pays 10 % and compounds semiannually?

2. How much should Don have in his pension fund today if he needs to withdraw $80000 annually in equal installments of $40000? Assume his investment fund guarantees a return of 10% and the fund compounds semiannually. Assume Don is 80 years old and expects to live to age 94.

3. How much should Don have in his pension fund today if he needs to withdraw $50000 annually in equal installments? Assume his investment fund guarantees a return of 6% and the fund compounds annually. Assume Don is 75 years old and expects to live to age 90.

Required) Calculate the amounts using the above scenarios using the manual method utilizing the tables.

I would like to request detailed explanations.

Answer 1

1)

Given,

Payment semi-annually =R=$12,500

i=rate=10%

n = no. Of years =14 years

Future value of annuity semi-annually =R[(1+i/2)n*2-1]/i

That is =R* Fv annuity factor

12500[(1+0.05)14*2]/0.05

=12500*(58.4026)

(Future value factor using future value annuity table at 5%,28years)

= 7,30, 032

In 14 years the fund will be worth $ 7, 30, 032.

2)

Installments =40,000

Years =14*2=28

Rate =10%/2=5%

Use present value of annuity formula

= A*i/[(1+i)n-1)] that is A*Pv annuity factor

=40000*pv annuity factor at 5%,28 years

=40000*14.8981

=$5,95,924

Therefore, in order to withdraw $40,000 semi-annually, he should have $5,95,924 today.

3)

Withdrawal amount =A=$50000

i=6%

Years =15 years

Use present value of annuity compounded anuualy formula

Pv = A*present value factor @6%,15years

=50,000*9.7123

=$4,85,615

In order to withdraw $50,000 annually, he should have $ 4,85,615 today.