Question

Cory Manciagli is planning to retire in 20 years. Money can be deposited at 6% compounded quarterly. What quarterly deposit must be made at the end of each quarter until Cory retires so that he can make a withdrawal of $40,000 semiannually over the first 10 years of his retirement? Assume that his first withdrawal occurs at the end of six months after his retirement.

Answer 1

It will require quarterly deposits of $ 171.06

Step-by-step explanation:

first we need to calcualte the present value of the retirement funds

and then, we will calcualte the PTM to achieve it.

1) present value of 40,000 semiannually over 10 years descounted at 6% cuarterly

`PTM * (1-(1+r)^(-time) )/(rate) = PV\\`

PTM 40,000 dollars

time 20 810 years x 2 payment per year)

rate 0.12 (0.06 x 2)

`40000 * (1-(1+0.12)^(-20) )/(0.12) = PV\\`

PV $298,777.75

Now, we calcualte which PTM generate this amount over the course of 20 years

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $298,777.74

time 80 (20 years x 4 quarter per year)

rate 0.06

`298777.75 / (1-(1+0.06)^(-80) )/(0.06) = C\\`

C $ 171.063