Present value refers to today’s value of a future amount.

**Present Value Formula:**

S

P = ————

(1+rt)

Instead of beginning with the principal which is invested, you could start from what you want to accumulate in the future, and then work backward to see the amount that you must invest to reach the required amount.

For example, if you wish to retire within a certain number of years you can begin working in reverse to determine what amount must be invested today to accumulate the desired amount at the time of your retirement in the future.

**Example**

Assume you need $20,000 in three years for a down payment on a house. If the simple interest rate is 5%, how much would you have to invest today to accumulate the $20,000 in three years?

In this example:

S= $20,000 (amount of maturity value)

t = 3 years

r = 0.05

The calculation for principal is:

S

P = ———-

(1+rt)

$20,000

P = ————-

[1 + (0.05)3]

$20,000

P = ————-

1.15

P = $17,391.30

Therefore, if you invest $17,391.30 today at 5% simple interest, you will have $20,000 in three years.

**Let’s check it out:**

Interest per year = $17,391.30 x 0.05 = $869.57

Interest for three years = $869.57 x 3 = $2,608.70

Therefore, the amount available for down payment at the end of three years is $17.391.30 + $2,608.70 = $20,000

**Instead of 5% simple interest, consider 5% compound interest payable semiannually:**

Formula to be used:

P = S(1+i)^-n

S = 20,000

i = 0.05 / 2 = 0.025

n = 2 x 3 = 6

P = $ 20,000(1+0.025)^-6

= $ 20,000(1.025)^-6

= $ 20,000 x 1

———

(1.025)^6

= $ 20,000 / 1.16

= $ 17,241.38

**Let’s check it out using the compound interest formula:**

S = P(1 + i)^n

= $ 17,241.38(1 + 0.025)^6

= $ 17,241.38(1.025)^6

= $ 17,241.38 x 1.16

= $ 20,000