![]() ![]() What to do when the Compounding Bases aren’t the Same Let’s take a look at what to do when the rate given is not the rate per compound period. One thing to note is that, because we were given an annual rate and were compounding annually, we were able to plug i and n into the formula directly. In this case, our total accumulated interest is $216.65 (once again, this is the sum of interest earned each year). All we have to do is subtract our present value from our future value because the future value is simply the present value plus interest. While our formula computes the future value, finding the interest portion is only one more step. The future value is calculated easily with our formula below: Now, you may be thinking that this seems complicated to compute and that it takes a lot of steps in order to arrive at what your $1,000 will be worth in five years, but thankfully, we have our formula to help us with this. ![]() What has happened here is that we have added our interest (the sum of the dollar amounts in Column “Interest”) to our initial principal or present value amount. After five years, you will have $1,216.65 in your account. The process is shown in the chart below.Īs you can see, the amount of interest increases each year as the balance of the account at the beginning of each year increases. We can replicate this same process over the course of a five-year period to see how things progress. We are earning interest on our previously earned interest rather than earning the same amount of interest each year. This means that you earned $41.60 in interest in the second year because you earned 4% on $1,040. Now though, we will choose to reinvest this interest, so in the second year, you will earn 4% interest on $1,040, which is the amount you will have after the first year. Just like with calculating simple interest, after one year, you will end up with $1,040 in your account because you have earned $40 in interest ($1,000 * 4%). The only difference here is that rather than sticking that interest in your pocket, you are reinvesting it. The first step in the calculation is exactly the same as with calculating future values with simple interest. Herein lies the power of compounding! Let’s look at the calculation. ![]() Because we are compounding interest, we must reinvest our interest earned so that our interest earned also earns interest. How much will you have after five years? In order to calculate the future value of our $1,000, we must add interest to our present value. ![]() Let’s say you invest $1,000 in an account that pays 4% interest compounded annually. If you are compounding daily, for example, then be sure that you are working with a daily interest rate, or if you are compounding monthly, be sure that you are working with a monthly interest rate. The only thing you must remember is that the interest rate must match your time period. The formula can be used when compounding annually, monthly, or at whatever time interval over which you wish to compound. The present value is simply the amount of money that will be invested, i is the interest rate for each time interval, and n is the number of compounding intervals. ![]()
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