Liam deposits 3500 in a saving account that pays 7frac12...

Liam deposits $\$ 3,500$ in a saving account that pays 7$\frac{1}{2} \%$ interest, compounded quarterly. a. Find the first quarter’s interest. b. Find the first quarter’s ending balance. c. Find the second quarter’s interest. d. Find the second quarter’s ending balance. e. Find the third quarter’s interest. f. Find the third quarter’s ending balance. g. Find the fourth quarter’s interest. h. What is the balance at the end of one year? i. How much interest does the account earn in the first year?

Transcript

00:02 All right, so here we have a interest compounded interest situation.

00:09 We have liam who deposits $3 ,500 in a savings account that pays 7 .5 % interest, and we're compounding it quarterly.

00:18 So let's just write, make a note of what's going on here.

00:22 We've got a formula.

00:24 The formula is the amount that you have is equal to the principal times one plus the rate, the interest rate, divided by the number of times compounded.

00:33 So what we're looking at is a rate of 7 .5 % as a decimal, so that'd be 0 .075.

00:40 And the number of times that we're compounding it is four times a year.

00:44 Our principal is $3 ,500.

00:47 So then we're using, for the first compound cycle, we're using the formula 3 ,500 times one plus that interest rate divided by four since it's compounded four times.

01:00 Times.

01:02 So when you enter that in your calculator, it's going to give you a value of $3 ,565 .63, which means the interest that we earned was $65 .63.

01:28 Now we're going to use that exact same formula, but we have a new amount.

01:34 That we're using as our principle.

01:36 So our new principle is this 356563.

01:41 So we're going to substitute that in here as our new principle 3565 63.

01:50 And we're going to multiply that times 1 .01875.

01:58 And that gives us a new amount of a new balance of 30 ,000 ,000.

02:04 36 3248.

02:08 So the interest that we earned is the difference between these two...