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dimaraw [331]
4 years ago
14

You want to purchase a new car in 5 years and you anticipate the cost of the car to be $55,000. You are given an investment plan

with a fixed APR of 6.2%, assuming that you make regular monthly deposits.  How much should you deposit at the beginning of each month to reach your goal of $55,000 in 5 years? Round to the nearest cent.
Mathematics
2 answers:
Usimov [2.4K]4 years ago
5 0
Wow - that is an unusual calculation.  You'll need a formula for the monthly payment of a monthly annuity, and it is located here:
http://www.1728.org/annuity3.htm  (see formula 2)
You'll find THAT page and THIS page very helpful:
http://www.1728.org/annuitym.htm


rate = rate / 1,200
rate = <span> <span> <span> 0.005166666667 </span> </span> </span>
n= number of months = 5 * 12 = 60

monthly amount = [Total] / ([(1 + rate)^(n+1) -1] / [rate]) -1

monthly amount =
55,000 / [[( 1<span>.005166666667)^</span>(61)-1] /  1<span>.005166666667] -1
</span>
monthly amount = 55,000 / [[<span><span>1.3693761617</span> -1</span>] / .005166666667]-1
monthly amount = 55,000 / [[.3693761617] / .005166666667]-1
monthly amount = 55,000 / ((<span> <span> <span> 71.4921603244)-1)
</span></span></span>monthly amount = 55,000 / (<span> <span> 70.4921603244)</span></span>
<span><span><span>monthly amount = 780.2286062293 </span> </span> </span>
OR 780.23 (rounded)

Yes, it's just that "simple". LOL


nasty-shy [4]4 years ago
4 0
I think the answer is 780.23 but im not sure if i made a calculation mistake.
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Find the sum of the infinite geometric sequence:<br>8, 4, 2, 1, .......​
tatyana61 [14]

Answer:

<h3>Therefore the sum if the series is 15.98!</h3>

The common ratio is 1/2 or 0.5 . If you multiply the current term by the the common ratio the the output will be the next term.

8⋅1/2=4

4⋅1/2=2

2⋅1/2=1 etc ...

because the absolute value of r is less than 1 we can use the following formula.

a/1−r where a is the first term and r is the common ratio

In our problem

a=8 and r=0.5

Substitute

8/1−0.5=8/0.5=16

The sum of this infinite geometric series is 16.

Also, another formula you can use that is guaranteed to work every time, no matter what, is:

Sn=a(r^n−1/r−1)

All the variables work the same way as above, and "n" is the number of terms in the series. So, say you wanted to find the sum of the first 10 terms and were to substitute everything in:

S10=8(0.5^10−1/0.5−1)

S10=15.984375

Therefore the sum if the series is 15.98!

Step-by-step explanation:

<h2>Hope it is helpful....</h2>
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