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Use the appropriate formula to find the value of the annuity: b. Find the interest: Rate Time Perodic Deposit 580 at the end of every six months 5.,5% compounded se...

Question

Use the appropriate formula to find the value of the annuity: b. Find the interest: Rate Time Perodic Deposit 580 at the end of every six months 5.,5% compounded semiannually 835 yearsClick the icon to view some finance formulasThe value of the annuity is (Do not round until the final answer; Then round t0 (he nearest dollar as needed )

Use the appropriate formula to find the value of the annuity: b. Find the interest: Rate Time Perodic Deposit 580 at the end of every six months 5.,5% compounded semiannually 835 years Click the icon to view some finance formulas The value of the annuity is (Do not round until the final answer; Then round t0 (he nearest dollar as needed )



Answers

Find the future value of each annuity due. Then determine how much of this value is from contributions and how much is from interest.
$\$1500$ deposited at the beginning of each semiannual period for 11 years at 5.6$\%$ compounded semiannually

We will solve this problem using this one over here. So part a of the question we're asked, how much will we have saved at the end of five years? So in order to find that we know we need to find the values for P R. On. So let's write those down. First, he is going to be equal to 2500 because that's how much we're putting in at the end of each year. Are is the interest rate, so that's 6.25%. So that is 0.0 65 and on a Z, a number of times compounded per year. So this is compounded annually, which means once per year and then lastly, T it is a number of years, so that's going to be five. So now we're going to put all these numbers into this formula here to find the value of the annuity. So that's going to be equal to 2500 times 1.625 to the power of five minus one, and we're dividing that by 0.0 six to. So we're going to punch this into a calculator. Fine likes one by 5.62 Right now we get this is equal to brownies. The nearest dollar 14 miles on 163 now part to be were asked if eyeing the amount of interest earned. So a lot of interest earned is going to be the total amount in the account, uh, minus the amount of money that we put it. So we're going to find the total amount of money put in that's going to be 2500 per year times a total of five years. So that's 12,500 which means interest is going to be equal to watching those of 163 minus 12,500 so they don't give us a total amount of 1666.

The money deposited in a sabbatical toe on a masters degree at the end of each year, which is the principal, is equal to $2500 while the number of terms is equal to one on the total time is off. Five years on the rate of interest is equal do 6.25% for Annam, which is equal to 0.6 to 5 Now we need to find how much will I save at the end of five years. So the amount will be given us equal toe being multiplied with one plus R, Divided by Endres to the part off NT minus one, divided by R, divided by n, which is equal to 2500 multiplied with one plus 0.625 divided by one raised to the part off five into one, minus one. Holding divided by 0.6 So five divided by one, which is equal to 14,163 $0.25. Now we need to find out the interest also, so the interest will be equal to the amount minus the principle for five years, which is equal to 14,163 0.25 Minus five multiplied $2500 which will be equal toe 14,163 $0.25 minus $12,500 which is equal to $1663.25.

The annual interest rate is our hand. Has the mass interest rate is our over drill. So after N. Men's there are. And deposit. And first deposits can be key times one class Are over 12 to the power of end amounts. And the second deposit can be p times one plus R. Over drill To a power and miners one amount and Alexandra. And the last deposit can be p times wow Plus are over 12 mountain man. So the some of this is just pierre times and plus are over child plus one plus are over 12 squared and etcetera into one plus r. over tell to the ants. Power. Not that they say that geometric sequence and has it's some echoes. The numerator is the first term times one. Miner's the common ratio to the power of And the denominator is one miners. The common ratio. So they're psychos, p times one class are over 12 over Miners are over 12 times Miners, one class are over 12 to use power and their sickles. Pierre times travel are plus one, and there is a minor sign here, so it should be One plus are over 12 to the inch, power -1. So this is a result we want.

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.


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