Mathematics, 13.11.2019 02:31 kenoknox

Find the future value of an annuity due of $700700 semiannually for fourfour years at 88% annual interest compounded semiannually. what is the total investment? what is the interest?

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Answer from: mareiashanti002

The future value of annuity is $27850302.48

The Investment amount is $ 37900.259

The compound interest is $ 662799.741

Step-by-step explanation:

Given as :

The due amount = $ 700700

the rate of interest compounded semiannually = 88%

The time period = 4 years

Let The investment principal = $ P

The interest = CI

Let The future value of annuity = FV

Now, The future value of Annuity method

FV = Amount × $\frac{(1+\frac{Rate}{2\times 100})^{2\times time}- 1}{\frac{Rate}{2\times100 }}$

Or, FV = $700700 × $\frac{(1+\frac{88}{2\times 100})^{2\times 4}- 1}{\frac{88}{2\times100 }}$

Or, FV = $700700 × $\frac{(1.44)^{8}-1}{0.44}$

Or, FV = $700700 × 39.7464

∴ FV = $27850302.48

Now, from compounded method

Amount = Principal × $(1+\frac{Rate}{2\times 100})^{2\times Time}$

Or, $ 700700 = P × $(1+\frac{88}{2\times 100})^{2\times 4}$

Or, $ 700700 = P × $(1.44)^{8}$

or, $ 700700 = P × 18.488

∴ P = $\frac{700700}{18.488}$ = $ 37900.259

So, Investment amount = $ 37900.259

Now,

Compound Interest = Amount - Principal

Or, CI = $ 700700 - $ 37900.259

Or, CI = $ 662799.741

Hence The future value of annuity is $27850302.48

The Investment amount is $ 37900.259

The compound interest is $ 662799.741 Answer

Answer from: Quest

throw the computer

step-by-step explanation:

Taking this quiz i’m stuck on this one me out

Answer from: Quest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.

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Find the future value of an annuity due of $700700 semiannually for fourfour years at 88% annual int...