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 correct answer is:

$263,123.19.

Step-by-step 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))/0.05] \\ \\=1200(1.05)^(49)+1200[((1.05)^(50)-(1.05))/ 0.05]=263123.19`

Answer 2

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