Question

If $3000 is invested at 9% interest, compounded annually, then after n years the investment is worth an = 3000(1.09)n dollars. (a) Find the first five terms of the sequence {an}. (Round your answers to the nearest cent.)

Answer 1

Answer:

The first five terms of the sequence are:

First year: $3270.00

Second year: $3564.30

Third year: $3885.09

Fourth year: $4234.75

Fifth year: $4615.87

Explanation:

When we're dealing with compound interest rates we're dealing with interests being re-invested into the original investment. This means that the new interests of one period will bear interests in the next period. This can be simply calculated using the compound interest formula.

The formula for compound interest rates is $P(1+i)^{n}$

Where:

P is the principal amount being invested,

i is the interest rate,

n is the number of years.

So for the first year we replace in the formula with the given values:

3000 × $(1.09)^{1}$ = $3270

And for the rest of the years we only need to modify the value of n.

For the second year we'd have:

3000 × $(1.09)^{2}$ = $3564.3

And so on.