To pay off an insurance settlement you must make monthlypayments of $2500 for 6 years. How much should you invest in anaccount paying 6% compounded monthly to be su...

How much money must be invested now at $9 \%$ per year, compounded semiannually, to fund an annuity of 20 payments of $\$ 200$ each, paid every 6 months, the first payment being 6 months from now?

In this question, the value of interest rate will be 0.6 divided by 12 because we're compounding that investment monthly. So 0.6 divided by 12 is equal to 0.5 No, the future value of anonymity given to us is $2000. I'm via investing it over eight months. So therefore, an is equal to eight now. Putting it in the formula F is equal to our into one place. I hold a spot and minus one, divided by our would be the investment made every month. So if it's 2000 one plus, I will be 1.5 Hold a spot eight minus one, divided by 0.0 It's like so one 1.5 they spot eight minus one Divide by 0.0 five is 8.1414 Therefore, our ability to 1000 divided by a 8.1414 So that is equal to $245.66

Okay. How much did you invest in a continuously compound ID account. Continuously compound ID at an annual interest rate of 6% if you want to exist. Want exactly $8000 after four years. Okay, so it's asking how much you should put in this account to get $8000 again, since we see compounded continuously, we're going to use our continuous formula or pert formula. So we want $8000. So that's our Y value. We don't know how much we're going to put in. He is just a number. And we have our rate point. 06 Remember to move that decimal point over twice and our time is four years. So we're solving for Pete here. We're solving for the initial value. So we have to remember that this right here is just a number. So what you're gonna d'oh is you're going to divide by that whole number. But you want to do it all together in your calculator and not round. Otherwise your answer's going to be skewed. Okay, so this will cancel because it's just the number when you divide 8000 by that whole expression e to the 80000.6 times for you will get $6293 and two cents. So that's how much you should put in if something's compound and continuously at 6% for four years to be able to make 8000 IRS.

So we're asked. Look at how much money must be invested right now at 9% a year. Compounded semi annually. Compounded semi annually to fund an annuity of 20 payments of $200 each paid every six months in the first payment is six months from now. Okay, so now that we have all of our information, we're gonna look at that and go through insult. So first we know that n or number of payments 20. We know that our new ity or payments of the A f is going to be $200. We also know that our interest rate or eyes 9% and that's going to be a fool 0.9 on a yearly basis. So we want to find that semi yearly so we'll just say that 0.9 and divided by two, which is going to give us 0.0 for five. Okay. And now that we have that we can go through and soul. So we know that the formula we're looking at is a sub f is our times one plus our interest to the ends and overpayments minus one over interest. So we're gonna have our ace of F our annuity is gonna be 200 equals R which we're not sure. Times one plus 10.45 to the end, just 20 and then minus one over. Not all that just up until here and then over 0.45 So when we get that, we need to rearrange that you are on one side. So when we do that, we have our which is going to be that 200 times 0.45 over 1.45 20 if power minus one. So our is gonna equal 200 times 2000.45 over 1.412 So then when we do that, we get our is 6.3739 So our semi annual investment is going to be $6.37 on this would be your answer

The formula for number of another payment on the investment. And they expressed as a This is equals toe the payment, especially times the quantity, one less I to the end. I am just one number. I This is a given problem formula for the M SM annually to that it off in the dress. Where is the East interest the Aniston number of on witty? This is the energy, the and the the number off annual payments. You know, each according to the problem. It has an energy off 20 payments off $200. So are Sequels to 200 and the end is on album that difficult 20 and also have the interests. This ice calls to 9% annually, and teams that it's problem stated that it's compounded some annually with the very way, too so interests will become 4.5 person. So here we have to substitute the values. This is from Letter A. So the value Any singles toe 200 times one glass shoot a point should have 45 our part to five thousands Here. Thank you. Whence one over sit upon. She reported five or 45 thousands. Now we have 280 is quantity here. So you have 200 times 2.412 I'm this one over three point support five. Yeah. Who will have the value off? 100 times? 31 point, I said. And participles toe 6200 74 0.20. Atheists. The are not enmity off the never A So we have now. The part has been sold. So first, the second number two that we have the You know. I mean so it has bean big so $200 in every six months. So it's all school semi annual compounding. So the annuity here is about $6274.28 as an annuity. And then the first thing they have bean six months from now. So it just bean and it It's made the answer, but it's six point. Yeah, toast happened for