Precalculus Question

Question

You invest $900 at 6% interest compounded annually. How much is in the account after 8 years, assuming that you make no subsequent withdrawal or deposit?

Answer 1

Compound interest is where you take the principal and g_{ive the interest successive times.}

Let the investment in an interest-bearing account be $900. Let the 6% interest be given on an annual basis.

Future Value = FV_yr

FV₁= ($990)*1.06 = $1049.40 after 1 year

FV₂=($990*1.06)*1.06 = $1112.36 after 2 yr Notice that FV₂ =$990* 1.06²

FV₃ =($990)* 1.06*1.06*1.06 = $1179 Notice that FV₃= $990*(1.06)³

So FV₈ =$990*(1.06)⁸ = $1577.91

This is the amount of value the account has after 8 years when the interest is applied once per year.