Question

You want to withdraw $500/month from an account for the next 3 years AND on the last payment, in addition to the $500 you also will receive $4,000. How much must be deposited in an account earning 18% in order to provide this cashflow. DRAW A TIMELINE, IDENTIFY THE TYPE OF TVM PROBLEM and solve.

Answer 1

1: Timeline

Year      0            1            2            3            …………………….36

CF          ?            500        500        500 ………………………… 4500

2: PVA and PVLS

We need to find the present value of annuity+ Present value of the lumpsum amount of$4000

3: PV = 500*(P/A,18%,36) + 4000*(P/F,18%,36)

= 500*(1-1/(1+0.18/12)^36)/(0.18/12) + 4000*1/(1+0.18/12)^36

= 500*27.66068 + 4000*0.58509

= 16170.70