Question

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 60th birthday and the last payment on your 79th birthday. You open an investment account on your 25th 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 25th birthday) and continuing until you are 40 years old (i.e., the last deposit is made on your 40th birthday). How much will each deposit have to be if you want to meet your financial goals?

Answer 1

Solution

Here Amount needed for 20 years i.e 60th to 79th year = 25000/year

Therefore Present value of the annuity when he will be 60 years of age will be

PV of annuity= Annuity value*{(1-1/(1+r)^n)/r)

=25000*[(1-1/(1+.09)^20)/.09)]

=228213.6

Now this value has to be discounted to 40 years of age as the payments will be deposited until 40 years

PV = Amount/(1+.09)^19= 228213.6/(1.09)^19=44385.2

The total amount that should be available by the time age is 40 = fund for kids+44385.2= 94385.2

Therefore this is the future value of annuity= 94395.2

Future value of annuity=Annuity*[(1+r)^n-1)/r)]

Here n=16 years

94395.2= Annuity*[(1+.09)^16-1)/.09]

Solving we get Annuity= 2859.86/year starting from 25th birthday