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zysi [14]
4 years ago
12

in the following ordinary annuity interest is compounded with each payment and the payment is made at the end of the compounding

period. find the accumulated amount of the annuity. 4,500 annually at 6% for 10 years
Mathematics
1 answer:
stealth61 [152]4 years ago
4 0

Answer: $59313.58

Step-by-step explanation:

We know that formula we use to find the accumulated amount of the annuity ( ordinary annuity interest is compounded ) is given by :-

FV=A(\frac{(1+\frac{r}{m})^{mt})-1}{\frac{r}{m}}), where A is the annuity payment deposit, r is annual interest rate , t is time in years and n is number of periods.

Given : Annuity payment deposit :A= $4500

rate of interest :r= 6%=0.06

No. of periods : m= 1   [∵ its annual]

Time : t= 10 years

Now we get,

FV=(4500)(\frac{(1+\frac{0.06}{1})^{1\times10})-1}{\frac{0.06}{1}})\\\\\Rightarrow\ FV=(4500)(\frac{(1.06)^{10})-1}{0.06})\\\\\Rightarrow\ FV=(4500)(\frac{0.79084769654}{0.06})\\\\\Rightarrow\ FV=(4500)(13.1807949423)\\\\\Rightarrow\ FV=59313.5772407\approx59313.58 \ \

∴ the accumulated amount of the annuity= $59313.58

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Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to).  We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:  

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

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We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points.  I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b  

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line:  y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2).  This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line:  (-3,-2)

y = -2x + b

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The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8

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Step-by-step explanation:

3x + 7 - x + 2 combine like terms

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Step-by-step explanation:

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