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Mariulka [41]
3 years ago
6

Jim and Dianna want to save for their child’s college expenses. They find an annuity that pays 6% annual interest, compounded mo

nthly.
If they invest in this annuity by contributing $300 per month for 10 years, how much money will they have for the college expenses?
Mathematics
1 answer:
lana66690 [7]3 years ago
7 0

Answer:

future value = $49163.8

so required amount will be $491200 nearest $100

Step-by-step explanation:

given data

annual interest rate = 6 %

annuity = $300 per month

time period = 10 years

to find out

how much money will they have for the college expenses

solution

we know that effective rate will be

effective rate = \frac{0.06}{12}

effective rate = 5 × 10^{-3}

number of payment = 12 × 10 = 120

so future value will be express as

future value = annuity × \frac{(1+r)^t-1}{r}   .........1

future value = 300 × \frac{(1+5*10^{-3})^{120}-1}{5*10^{-3}}

future value = 300 × 163.8793  

future value = $49163.8

so required amount will be $491200 nearest $100

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Hi

609.9 ⇒ 85%
x ⇒ 100%

85x = 100·(609.9)
85x = 60,990
x = (60,990)/85
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85% of 717.53 ⇒ 0.85 × 717.53 = 609.9005 ≈ 609.9

Answer: 717.53
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True

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Simplify. 10 + 51 -10 + 51 41
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3 0
2 years ago
A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How
Mazyrski [523]
Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:


In the year 1985 the worker earned <span>$10,500. 

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

                                            $10,500(1+0.06).



In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]=$10,500(1.06)^2.


Similarly we can check that in the year 1987 the worker earned $10,500(1.06)^3, which makes the pattern clear. 


We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}.

Factorizing, we have

=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r}) (where a is the first term and r is the common ratio) we have:

\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17.



Finally, multiplying 10,500 by 59.17 we have 621.285 ($).


The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating (1.06)^{26}.


Answer: D



4 0
2 years ago
Help please i need to know this
Harlamova29_29 [7]

Answer:

As shown in the attachment,

Step-by-step explanation:

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