Quiz week 3 - 401(k) & investing a 6. if a person starts investing $100 per month starting at age 21, and that money earns a 7% return every year, how much will this person have when turning 70 years old? for ease of calculation, assume starting balance of $0 and annual contributions of $1,200 (12*$100).

To solve this problem, we use the formula:

F = A [(1 + i)^n – 1] / i

where,

F is the future value or the amount he will have

A is the amount he invest each year = 1200

n is number of years = 70 – 21= 49

i is the interest or return rate = 7% = 0.07

 

Hence the value of F is:

F = 1200 * [1.07^49 – 1] / 0.07

F = $454,798.80 

This can be solved by a formula for compound interest wherein:

A = Expected amount
i = interest raten = annual depositst = timed = initial deposit amount
A = d { [(1 + i/n )nt+1 - (1 + i)] / i }A = 100 { ((1 + 0.00583)841 - (1 + 0.00583)) / 0.07 }A = 100 { (132.793 - 1.0053) / 0.07 }A = 188268 
The final amount would be 188268 dollars after he has already turned to the age of 70 if he would start investing in this investment medium when he is only 21.