Question

1. You are currently 25 years of age. You have developed a lifetime budget that includes $50,000 at age 40 for a college fund for your kids and $25,000 per year for 20 years to supplement your retirement, the first payment on your 60^th birthday and the last payment on your 79^th birthday. You open an investment account on your 25^th birthday that promises to pay 9% interest compounded annually. You want to deposit equal annual amounts into the account every year on your birthday, starting today (your 25^th birthday) and continuing until you are 40 years old (i.e., the last deposit is made on your 40^th birthday). How much will each deposit have to be if you want to meet your financial goals?

I am struggling with annuity due and ordinary annuity so if you could please emphasis that within the solution.

Answer 1

25 yrs ---->--- $50,000 at age 40--->------60 yrs-->-20000/year-->--79yrs

We need 20000$ for 20 years for retirement

At 60 we required the money of....

PV for 20 yrs, 25000$ at 9%=  $ 228213.64

The present value of above amount in 40yrs =

PV of $228213.64 for 20yrs (40 to 60) at 9%= 40720.36$

We need 50000 for child education at 40 yrs + 40720.36$ for retirement

50000+40720.36$= 90720$ ( Required at 40yrs old)

Future value = Periodic payment * {[(1+r)^n] - 1)/r}

pmt for 15 yrs at FV=90720$ and 9%

Periodic payment from 25th yr =3089.82$ per month