Question

If a person starts investing $100 per month starting at age 21, and that money earns a 5% 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).

Answer 1

The formula for calculating compound interest with yearly contributions is:

Balance = X*(1 + Y)^n + Z((1 + Y)^(n + 1) - (1 + Y)/Y)

where the balance is the money earned after n years invested

Y is the interest rate as a fraction

Z is the yearly contribution

X is the starting investment

Therefore the calculation for this example is:

Balance = 1200*(1 + 0.05)^48 + 1200((1.05)^49 - (1.05)/05)

= $249,393.5

Answer 2

The correct answer is:

$263,123.19.

Explanation:

The formula for compound interest with contributions is:
$T=P(1+r)^n+c[((1+r)^{n+1}-(1+r))/r]$,

where P is the starting principal, r is the interest rate, c is the yearly contribution, and n is the number of years.

For this problem, he starts out depositing $1200; this is P.

He contributes $1200 per year; this is c.

The interest rate is 5%; 5%=5/100=0.05.  This is r.

He starts at age 21 and we want to know how much he will have at 70:
70-21=49.  This is n.

This gives us:
$T=1200(1+0.05)^{49}+1200[((1+0.05)^{49+1}-(1+0.05))\div0.05] \\ \\=1200(1.05)^{49}+1200[((1.05)^{50}-(1.05))\div 0.05]=263123.19$