Your goal is to have 20,000 in your bank account by the end...

Your goal is to have $20,000 in your bank account by the end of nine years. If the interest rate remains constant at 3% and you want to make annual identical deposits, how much will you need to deposit in your account at the end of each year to reach your goal? (Note: Round your answer for PMT to two decimal places.) ? $2,165.55 $2,362.42 $1,574.94 ? $1,968.68

Transcript

00:01 Alright, so in this particular problem you are asked to find the interest given in the following scenario.

00:09 You've got $3 ,000 principal that you're investing.

00:12 Your interest rate is 2 .25%.

00:16 You're leaving it there for 10 years and it's compounded monthly.

00:20 So this is key right here.

00:23 We're looking for compound interest.

00:27 So to find the amount that we have, the formula for compound interest, the amount that we have is equal to the principal, the amount that we start out with, times 1 plus the rate divided by the number of times compounded raised to the number of times compounded times the length of time that we keep it there.

00:55 So this is our p, this is our r, this is our t, and our n comes from here.

01:04 In this case compounded monthly, so n equals 12.

01:10 So then we're just going to substitute in the amount that we have is equal to our principal times 1 plus our rate.

01:24 We have to write that as a decimal, so we're going to want to write it like that, changing that percent to a decimal, so .0225 divided by 12 since we're compounding it 12 times a year, monthly, and then that's raised to the 12 and we're leaving it there 10 years.

01:45 So 12 times 10.

01:48 And then we just calculate this.

01:52 So we're going to go to our calculator.

01:55 Let me go a little bit.

01:56 Alright, so we go to the calculator here and we say 3000 times 1 plus .0225 divided by 12, and then we're going to take that and raise that entire quantity to the 12 times 10.

02:36 So that gets us $3 ,756 .18.

02:45 $3 ,756 .18.

02:56 And we started with $3 ,000, so the amount of interest that we earn is $756 .18.

03:12 Now the second part of this problem says, okay, suppose we have compounded interest again, we are saving for a $40 ,000 down payment.

03:21 This time we want to know how much we need to invest.

03:24 If our rate is 6%, our time equals 12 years, we're compounding quarterly, so that means n equals 4...

Question

Please give Ace some feedback