It is now January 1, 2015; and you will need $1,000 on January 1, 2019, in 4 years. Your bank compounds interest at an 8% annual rate. How much must you deposit today to have a balance of $1,000 on January 1, 2019? The formula method for this questions is

Pv = $1000 (1.08) ^-4

Explanation:

Compounding is the computation of the future value of $1 invested today while discounting is the determination of the present worth of $1 in the future. Both are related by the equation

Fv = Pv (1 + r) ^n

where Fv = Future amount

Pv = Present value

r = rate of return

n = time in years

Hence the formula required

$1000 = Pv (1 + 0.08) ^4

Pv = $1000 (1.08) ^-4

You need to deposit $735.03 today

Explanation:

Future Value (FV) : $1,000

Rate: 8% pa

Tenor: 4 years

Present value is the amount of deposit today?

FV = PV * (1 + rate) ^ tenor

⇔ 1000 = PV * (1+8%) ^4

⇒ PV = 1000 / (1+8%) ^4 = $735.03