Abby Mia wants to know how much must be deposited in her local bank today so that she will receive yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.

Future value, F = 18000

interest rate (APR) = 9% compounded annually

n=20 years

P=present value.

We know from the compound interest formula that

F=P (1+i) ^n, in other words,

P=F / (1+i) ^n

=18000 / (1+0.09) ^20

=$3211.756

You can round to the desired accuracy as you wish.

It's annuity problem

To solve your question use the formula of the present value of annuity ordinary which is

Pv=pmt [ (1 - (1+r) ^ (-n)) : r]

Pv present value?

PMT yearly payments 18000

R interest rate 0.09

N time 20 years

So

Pv=18,000 * ((1 - (1+0.09) ^ (-20)) : (0.09))

pv=164,313.82