00:01
For this question, we're given that a person invests $5 ,000 in an account that earns 4 .5 % interest rate, and i want to determine the value of the account after first 10 years compounded annually, 10 years compounded semi -annually, and 10 years compounded continuously.
00:20
So let's start with 10 years compounded annually.
00:23
So in order to answer this question, i first need to understand the formula for compound interest.
00:29
The formula says a equals p times 1 plus r over n to the power of nt.
00:37
Now in this formula, a is going to be the final amount.
00:46
P is the principal, which is the initial amount.
00:53
R is the rate.
00:56
N is going to be the number of times interest is applied per period and t is going to be the number of time periods elapsed so applying the formula for the compound interest we have that a the final amount is going to equal the principal which i know is $5 ,000 since that was the initial amount in the account times 1 plus r so i know that r is 4 .5 percent which is the same thing as 0 .045 divided by n.
01:38
So in this case, i'm only compounding annually, so i'm only compounding once.
01:42
So that's just divided by 1 to the power of nt.
01:46
So to the power of 1 times t, which is 10 years.
01:52
So this is the same thing as just saying a equals 5 ,000 times 1 plus 0 .045 to the power of 10.
02:07
So now compute this value in a calculator to get a...