Financial Management
In order to determine the size of equal, annual, end period deposits needed to accumulate a specific future sum at a specific future date, several steps are required. This type of equation involves working backwards from the solution that you wish to find. Thus, if you want to accumulate $2,000,000 in ten years, this is the end result from which the remainder of the equation will be derived.
The payments are annual, equal and end of period. This fits the definition of an annuity, so it is the annuity formula that we will use to derive the required interest rate in order to bring the payments to the end result of $2,000,000 in ten years. In this example, the interest rate is to be taken as a given, and the solution derived should therefore be the sole remaining unknown variable, the size of the payment. To derive this solution, an interest rate of 8%...
is the periodic payment; n is the number of payments and I is the interest rate. Plugging in the values given, the formula would be:
2,000,000 = R [((1.08)^10 -- 1)/.08]
From this point, the bracket beside R. can be derived into a simpler numeral.
(1.08)^10 = 2.15892
2.15892 -1 = 1.15892
1.15892 / .08 = 14.4865
This leaves the original formula as follows:
2,000,000 = R (14.4865)
From which we can derive R, the periodic payment:
2,000,000 / 14.4865 = 138,059
There are a couple of important things to remember about this formula. The first is that the last principle payment, at the end of year 10, is included in the $2,000,000, but…
