Single payment formulas

Formula:

F = P(1+i)ⁿ

This is the single payment compound amount formula and is written in functional rotation as:

F = P(F/P, i, n)

P = F(P/F, i, n)

Example:

If $5000 were deposited in a bank saving account, how much would be in the account three years hence if the bank paid 6% interest compouded annually?

Solution:

We can draw a diagram of the problem. note: to have a consistent notation, we will represent receipt by upward arrows (and positive signs), and disbursement (or payment) will have downward arrows (and negative signs).

From the view point of the person depositing the $500, the diagram is:     

            

We need to identify the variuos elements of the equation. The presentsum P is $500. The interest period is 6%, and in three years are three interest periods. The future sum F is to be computed.

P = $500                        i=6%             n = 3                      F = unknown

F = P(1+i)ⁿ   =  500(1+0.06)³

=$ 595,50

If we deposit $500 in the bank now at 6% interest, there will be $595,50 in the account in three years.