Angela puts 1,000 in a savings account that pays 3 percent per year. What is the future value o

Angela puts 1,000 in a savings account that pays 3 percent...

Key Concepts

Future Value Calculation

Future value calculation involves determining the amount an investment or deposit will grow to over time by applying an interest rate. This calculation is crucial in financial planning, as it quantifies the growth of money, helping to assess the benefits of savings and investments over time.

Interest Rate

An interest rate is the percentage at which money grows over a specific period. It is used to calculate the extra amount earned, or owed, on a principal sum, making it a key factor in evaluating investments, loans, and savings.

Time Value of Money

This concept refers to the principle that money available now is worth more than the same amount in the future due to its potential earning capacity. It underpins many financial decisions, emphasizing that the opportunity to earn interest or returns on investments over time adds value to present cash.

Transcript

0:00 All right.

00:01 So the question we're looking at today is we have a sum of $1 ,000.

00:06 So $1 ,000, and it is placed in a savings account at 7 % per annum.

00:15 How much is in the account after 20 years if the interest is compounded? so this is a two -part question.

00:23 We define first a, how much would be in the account after 20 years of the interest was compounded annually? and b, how much would be in the account after 20 years at the interest was compounded annually? and b, how much would be in the count after 20 years at the interest.

00:31 Trust is compounded quarterly.

00:34 So for this question, we are going to use the same formula that we've been using for most of this section, which is a is equal to p, and our principle is always going to be the $1 ,000 that we start with, 1 plus r to the power of n.

00:53 So for the first one, a, which is annually.

01:02 So for this question, we're going to plug in our formula first.

01:06 So we have a thousand, and then times one plus our interest rate is 0 .07, and then that's to the power of 20, because that we're looking at 20 years.

01:19 So now this is equal to 1 .00, 0 ,000, oh, not 0, too many zeros, 1 .07 to the power of 20.

01:33 And when you put this into your calculator, you should get that the amount is equal to 3 .07 .3 .5.

01:46 3889 .68.

01:49 So that is the amount if the interest is compounded annually for 20 years...

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