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For the following ordinary annuity; determine the size of the periodic payment: Present Payment Conversion Future Value Value Period Term of Annuity Interest Rate P...

Question

For the following ordinary annuity; determine the size of the periodic payment: Present Payment Conversion Future Value Value Period Term of Annuity Interest Rate Perlod S15,800.00 quarter 13.5 years 10.1% quanenyThe periodic payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values t0 six decimal places as needed )

For the following ordinary annuity; determine the size of the periodic payment: Present Payment Conversion Future Value Value Period Term of Annuity Interest Rate Perlod S15,800.00 quarter 13.5 years 10.1% quaneny The periodic payment is $ (Round the final answer to the nearest cent as needed. Round all intermediate values t0 six decimal places as needed )



Answers

Find the future value of each ordinary annuity, if payments are made and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
$R=42,000 ; 10.05 \%$ interest compounded semiannually for 12 years.

Calculate the future value of a ordinary annuity. So the payments being put in our $800 the interest being calculated is 6.51 percent and the number of years there's 12. Now the add a piece of information here is that, uh, it's calm, pounded semi annually, so semi annually means, uh, it's happening twice per year. So are in for a formula will be double since it's happening twice per year and our interests will be half because it's happening twice per year. So our interest is gonna be 0.0, uh, three, 755 We just double check that. No stooping to 55 to Okay, So our formula for now, but we have everything set is our 800 times one plus our interest rates of 1.3 to 5 to the eighth Power, which is 24 tu minus one and then divided by our interest rate says 0.3 55 Okay, so it's just gonna equal 800 times. And I was gonna put all that in our calculator. So you at 1.3 to 55 to the 24th power minus one, but about 0.3 to 55 Is that total amount? Our multiplier is gonna be 35.5. Foreign. Some change came out to bind. About 800 gives us our total future annuity. It's 28,438 on and 21 sets. Yes, that's our total. Okay, so from our contributions, it's called C. We just need 800 we made 24 deposits, So 800 times 24. 19,200 star amount from contributions was 19 19,200. Which means if we subtract that from our total, we will get how much interest paid out. The interest paid out. 9238 and I got that bus just attracting our contributions from our total case in interest paid 9238 and 21 cents. Our contributions was 19,200 for a total annuity of 28,400 bus. Okay, thank you very much.

Because this phone it wants us to find the future value of the ordinary. Well, annuity. When the our value is equal to 9200 our interest rate is equal to 10%. Her 0.10 and we're gonna go for in seven years. Okay, Because this is semi annually, I'm just gonna put it s a It's gonna change. Our interest rate s were divided by two interest rate of 0.5 and the number of times it'll happen. Number seven years is equal to seven times two for semiannual. So in will equal for team keeps everyone plug it into our formula. Where the future total B 9200 times one plus R 10.5 So 1.5 to the 14th power minus one to about about 10.5 Okay, so, putting the decibel partner calculator, we have 1.5 to the 14th Power is gonna give us 19.598 Instant change. I have 9200 times 19 point. Yeah, 598 and some change. Okay. Is that grand total three multiplied by 9200 180,000 $307. Time. 41 cents. Yes, that's our future. Total. Next for this question. Says, determine how much values from contributions and how much is from interest. Well, contributions is fairly simple. We did 14 cup contributions of 9200. So 9200 times 14 is 100 28,800. Okay, so the amount from interest would just be taking a 180,000 amount in subtracting are 128,000 amount. So the amount from interest was 51,507. 41 sentence. Okay, so this is our contributions. This is our interest. And this is our terrible. Okay, thank you very much.

This one wants me to find the future value of an ordinary annuity. Uh, the contributions each period is gonna be $4600. The interest rate on this account is 8.73%. In the number of years. We're gonna leave it in the account. Ah, is nine okay? And the other piece of information give us is that this is a quarterly com pounding, which means that happens four times a year. So it's gonna turn my end value. My number of periods to be multiplied about four. My interest rate would be divided by four. So she is a calculator and get that real quick. So that interest rate will be 0.218 to 5. Okay, Just keeping all the deaths most cause we're raising into the 36 power. So we just got to make sure we keep our accuracy. So our formula for the future value is our our value 4600 times one plus our interest rates at 1.218 to 5. Race to the end power, which is 36. Subtract one from that value and then divide by our interest rate of 0.21 8 to 5. Okay, just putting that part into our calculator, think of us 53.85 and some change when they keep that change in my calculator and my next I would just be the multiply by 4200 which is gonna give us 226,000 208 on and 98 sets. Okay, again, you got to make sure you keep track of your, um, interest rates, because if that interest rate you say you rounded it to 0.0 to 2, um, it could change. That's this total value by a time. Okay, so the rest of this problem wants us to find out how much our contributions are. So for that, we just multiply 4600 times, 36 contributions, but and 4600 times 36 is 165,600. Some of my mark that over the seas are contributions were that much are total was this much our interests would just be the difference. So we've seen this subtract those two values and I still have another value saved in my calculator, so I can just go back to that. I'm subtracting 1 65 600 And so our total interest payments for 60,000 600 A and 98 cents, okay?

It's been a calculate. A present value, given that purity payment about you are are is 18,579 uh, paid into an ordinary annuity that has 5.4%. That's compounded semi annually. The reason I value 0.27 That's over half of that interest rate, and there are a number of periods is gonna be two times the number of years. Okay, so two times eight is 16 years. Okay, so RPI value Ziegel to r 18,005. 79 times one minus 1.27 to the negative. 16th power divided by 0.27 Okay, so he's got put that in our calculate here of 18 5 79 1.27 to the negative 16th power. That's gonna give us 238,000 $816 and 23 cents. Okay, thank you very much.


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