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Jasica Parker would like to have $84,000 to buy a new car in 7years. To accumulate $84,000 in 7 years, how much should sheinvest monthly in a sinking fund with 3% i...

Question

Jasica Parker would like to have $84,000 to buy a new car in 7years. To accumulate $84,000 in 7 years, how much should sheinvest monthly in a sinking fund with 3% interestcompounded monthly?

Jasica Parker would like to have $84,000 to buy a new car in 7 years. To accumulate $84,000 in 7 years, how much should she invest monthly in a sinking fund with 3% interest compounded monthly?



Answers

Hsu-Mei wants to save $\$ 5,000$ for a down payment on a car. To the nearest dollar, how much will she need to invest in an account now with 7.5$\%$ APR, compounded daily, in order to reach her goal in 3 years?

In this problem, Bob is going to deposit money each year. So this is a case of a periodic deposit investment account, not a single deposit. So we're going to use this periodic deposit investment formula, and we know that he wants to get $50,000 after seven years. We know his interest rate 4.2% and that is compounded annually, and that means one time a year. So in is one. So we're going to substitute all those numbers into our formula. We have 50,000 times. The interest rate changed into a decimal, which would be 0.4 2/1, divided by one plus 10.4 2/1 to the power of one time seven minus one. Now we could simplify that whole thing if we want to, before putting it in the calculator, because there's no need to have the divided by ones in there. So a 50,000 multiplied by 0.42 and divided by the quantity one plus 10.42 to the seventh power minus one. Go ahead and put that in the calculator and you end up with $6292.16 would be his annual deposit in order to ensure he ends up with his $50,000 at the end of seven years.

They're sinking fund problem. Uh, we have the amount trying to save for is $20,000. We're looking for the our value. We know the interest rate is being compounded quarterly, so needed to be done before. So 3.2%. So that's gonna point point 0.8% which is 0.0 a shows compounded quarterly and our number of periods. Because it's six years quarterly, our number of periods will be 24 periods. Okay, so we're gonna have 20,000. Sorry. Uh, equals R R value times one plus our interest rates at 1.0 a to the 24th power Tu minus one live at a bad point. 0.8 Okay, so that's gonna be 20,000 because my our value times we could put that in the calculator. Now, whatever. He's going to 26.34 and some change. Keep that number in our calculator and divide both sides by it. So we have 20,000 divided by our interest rate number. So it's gonna be her deposit. Needs to be, um r equals $759 and 21 cents. Okay. Thank you very much.

Whenever we see annuity problems like this one, we should immediately think of the equation. A is equal to p Times one plus I raised to the end power minus one, divided by I. This is given at the end of the most recent chapter of the book, and it's incredibly useful. So here, let's see what we have for each of the variables. First off A. We know that in 10 years we want to have $50,000 in the account, so a is going to equal to $50,000 then p How much are we paying for, period? Well, we don't really know. That's what we're solving for, so we'll leave P blank for now. Then I So I is the interest rate divided by how many times were compounding for years. So the interest rates is 6%. However, 6%. That's equal to 0.6 and then we have to divide by the number of times we're compounding. That is 12 times because we're compounding monthly in their 12 months per year. So I is equal the 120.0 6/12 and finally end and is the number of times this will be compounded. It's the number of periods that we want to have. So we have 10 years times 12 months per year, which will give us 120. So enter the 120 different payment periods. Now that we have all this information we can plug in and solve for Pete. So we have 50,000 is equal to P times. All right, one plus I. That is one plus point No. 6/12. Race to the end power where n is 1 20 minus one, divided by 10.0 6/12. And now that we have this, let's solve and rear entropy. So I plugged this entire term here on the right, into my calculator to get this, we now have 50,000 equals p. Times 1 63.88 and now dividing both sides by 1 63.88 will give us our final answer. P equals $305.10. So if we want to have $50,000 in 10 years, we should put in $305 every month into this account.

Okay, so we're given that Ashley has 12 or 120,000. She decides to invest well, she decides to put some into a CD that earns 4% interest per year. So assume that X is equal to, um, the amount invested in the city. So we have that, um, that's equal to X. And then we want to know the amounts invested in or low risk cock that 7% interest. So it's put this as 4%. So out of our total 120,000 Well, we're going to subtract that from the amount invested from our city, and that's gonna be equal to for amounts invested at seven presents. Right? Because we're only investing in two accounts and our amounts invested is a total of 120,000. So we want to know how much you earn If she invested each to earn interest of 7800. Okay, so let's set these equal to each other. Let's have 4% which is their 40.4 times X. We're gonna add that to the amount invested in our several presents. So that's 0.7 times 120000 and this is minus X and we have that the total amount earned. It just is $7.800. Okay, so let's see, um, let's multiply through that points where All seven times 120000 So he gets to a 0.4 x plus 8400 minus 0.7 That's people to 78 It was Oh, so that's isolates are constant. So I'm going to surcharge its halogen, or 8400 on both sides, and combine 84000.0 for minus 2.7 That's a negative 0.3 X is equal to 78 year old girl when it's 8400 So that's equal to negative 600 analysis. All forex, when we have to do is divide by 0.3 The negative of that, and I get that X is equal to make 600 divided by points or negative points 03 and that's equal to 20,000. So 20,000 is amount invested in our city, and then the amount invested in or seven percents. It's 1200. Our star 120,000 minus 20,000 which is equal to 10 dozen is the amount invested. This is interceding and this is in our low risk stock.


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