To find the amount A in an account after t years with principal P and an annual interest rate r

To find the amount A in an account after t years with...

Key Concepts

Compound Interest

Compound interest is a method of calculating interest where, after each compounding period, the earned interest is added to the principal so that the interest in the next period is calculated on a larger amount. This leads to exponential growth of the investment over time, as both the original principal and accrued interest earn returns.

Annual Interest Rate

The annual interest rate represents the percentage of the principal that will be earned as interest over the course of one year. When interest is compounded more frequently than annually, this rate is divided by the number of compounding periods to determine the periodic interest rate.

Compounding Frequency

Compounding frequency refers to the number of times in a year that interest is calculated and added to the account balance. A higher frequency of compounding results in faster growth of the investment, because interest is increasingly calculated on both the initial principal and the accumulated interest.

Time Period

The time period is the duration over which the investment grows, typically measured in years. In compound interest calculations, the effect of the time period is exponential, meaning that the longer the time, the more significant the accumulation of interest will be.

Transcript

00:01 All right, today we're going to talk a little bit about compound interest.

00:02 Let's find the amount of money an account would have after x years of compounding interest.

00:08 Okay, so we're going to start by first identifying the formula.

00:12 A equals capital p multiplied by 1 plus the r, the rate, to the t power.

00:18 Now, of course, any formula is no good unless you have some sort of context and what that stuff actually means.

00:23 So let's quickly break down what each of those letters means.

00:27 The a is the account amount.

00:28 It's different than simple interest because with the simple interest formula, you're looking for the interest only.

00:34 But this formula actually gives you the amount in the account after the formula has been applied.

00:39 So the a stands for the account amount.

00:42 The p stands for the principal, which is how much money you've actually invested at the beginning.

00:47 And the r is your rate of interest right here.

00:50 And then the t is a raised t.

00:53 It's an exponent.

00:54 It's the time frame the interest is compounded.

00:57 Now quickly, just what compounded means is when you earn interest on previously earned interest in addition to the principal.

01:05 So it's more than just what you start with.

01:07 So next, we're going to talk about an example problem.

01:10 And it says right here that ben's grandparents put $1 ,000 into a 1 % interest account that compounds annually when he was born.

01:20 How much money is in his account on his 18th birthday? again, i have the formula down here.

01:26 Let's just work it out really quickly...

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