Can someone explain when to use these formulas. Like what specific situation.

(Future Value) FV = S * (1 + r ) ^ n

(Present Value) PV = S * [1/(1 + r)^n]

(Future Value Annuity) FV = A * [(1+r)^n) ? 1]/r

(Present Value Annuity) PV = PV = A * [ 1- 1/ (1+ r ) ^ n ] / r

Can someone also explain the answers to these problems. Only Exercises 3.1 and 3.2 are needed. The pictures are the questions and the pdf shows the solutions.

Solutions Chapter 3 Exercise 3.1 a. PV of withdrawals = $4,000*(1 - 1/1.066 )/0.06 = $19,669.30. FV = ($20,000 - $19,669.30)*1.066 = $469.11. b. PV at end year 2 of withdrawals = $4,000*(1 - 1/1.066 )/0.06 = $19,669.30. PV today = $19,669.30/1.062 = $17,505.61. FV = ($20,000 - $17,505.61)*1.068 = $3,975.68. Or $20,000*1.062 = $22,472 = FV one year before first withdrawal. ($22,472 - $19,669.30)*1.066 = $3,975.68. Exercise 3.2 PV of 20 withdrawals = $12,000*(1 - 1/1.0620 )/0.06 = $137,639.05. This is the amount the fund must hold one year before the first withdrawal. Using [4] we set the FV of the 15 deposits equal to this amount. D*{(1.06)15 - 1}/0.06 = $137,639.05. D = $137,639.05/23.276 = $5,913.35. Exercise 3.3 a. $25*(1.015)5 = $26.932m. b. PV = $26.932/(0.06 - 0.015) = $598.49m.