Step-by-step explanation:
it is very simple : that means what ever balance you had last year, the one for the following year is then 1.03 times the balance at the end of last year.
that happens every year.
so, at year 0 you pay in the initial amount ($6,500).
at the end of the first year you have
6500 × 1.03
at the end of the seconds year you have
(6500 × 1.03) × 1.03 = 6500 × 1.03²
at the end of the third year you have
((6500 × 1.03) × 1.03) × 1.03 = 6500 × 1.03³
and so on.
that means our function for the investment balance over t years looks like
I(t) = 6500 × (1.03)^t
A.
what does the growth factor mean ?
1.03 = 1 + 0.03
1 stands simply for the unchanged last amount (x × 1 = x), and 0.03 is the part of the whole last amount we add.
0.03 = 3/100 = 3%
the growth rate is 3%.
B.
now we use our function I(t) for t = 25 years :
I(25) = 6500 × (1.03)²⁵ = $13,609.55654... ≈ $13,609.56
