Question

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

Answer 1

Pv = $1000 (1.08)^-4

Step-by-step 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

Answer 2

You need to deposit $735.03 today

Step-by-step 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