At what age would Robert have $1000000 in this account?

Question

15. Robert set up an investment account when he was 18 years old. He put $500 a month into the

account for 12 years. This account paid an average annual rate of interest of 5.75%

compounded quarterly for the 12 years. At the end of the 12 years, at age 30, Robert took all

the money from this investment and put it into a different account that paid a fixed annual rate

of 7% compounded annually as long as he did not withdraw any of the money. At what age

would Robert have $1000000 in this account

Answer 1

N = ln  (1,000,000 / 62,009.71) /  ln (1.07)

 

= 0.478 / 0.0676

 

= 7.06

 

Now add this value to his present age and you come up with 37 years.  It took me with while to figure it out but I finally got it. 

 

 

Answer 2

First you have to find the amount of an ordinary annuity whose variables are:

 

PV =  0

PMT = 500

N = 144 months

i% = 5.75% / 12 = .47916667%

FV = ?

 

A financial calculator solves this most easily. You can also use a spreadsheet function or a formula.

 

The Amount, or Future Value of the annuity is 62,009.71

 

This amount is now invested as a single sum and allowed to grow at 7%. the variables are

 

PV = 62,009.71

FV = 100,000

i% = 7%

PMT = 0

N = ?

 

Here the formula is FV = PV (1 + i%)^N

100,000 = 62,009.71 (1.07)^N and you have to solve for N.

 

The calculators gives us the solutions. N = 7.06

 

So he will be 37 years old when the fund reaches $100,000.