It's a simple time value of money problem, you just find the present value of both amounts (assuming monthly compounding) We must change the annual interest rate to a monthly rate ,,,rate/months

Using the basic equation FV=PV(1+r/m)^t*m and rewriting is as PV=FV/(1+r/m)^t*m

so PV=1800/(1+.12/12)^18=1504.83

and PV=2400/(1+.12/12)^36=1677.42

to equal 3182.25 to be deposited today.

to verify 3182.25*(1.01^18)=3806.44 this is the amount available on month 18

a withdrawal of 1800 on month 18 gives us a new balance of 2006.44

2006.44*(1.01^18)=2400 available month 36 minus 2400 which equals 0.

Hope this helps

Instead of equations, you could use the TMV tables for the Present Value of $1.

a) N 18, Rate 1%, Factor 0.8360 x 1,800 = 1,504.80

b) N 36, Rate 1%, Factor 0.6989 x 2,400 = 1,677.36

Total required to deposit today (it's PV) = 3,182.16

A woman plans to withdraw $1800 18 months from now and $2400 36 months from now. How much does she need to deposit today if the interest rate is j12= 12%

I really need to know the steps as to how this type of question is answered so please explain as to how you got the answer, thanks