# American general offers a 7-year ordinary annuity with a guaranteed rate of 6.35% compounded annually.

###### Question:

## Answers

$ 55135.978

Step-by-step explanation:

At most, the present value of annuity must be paid. So we must find the present value of the annuity

Given in the problem, we have:

Periodic Payment = PMT = $10000

Rate of interest annually = i = 6.35 %= [tex]\frac{6.35}{100}[/tex]=0.0635

no. of periods= n=7

So to solve this, we need to use the present value formula:

Present Value = Periodic payment [tex]\frac{1-(1+rate.of.interest)^{-n} }{rate.of.interest}[/tex]

Present Value = PMT [tex]\frac{1-(1+i)^{-n} }{i}[/tex]

Present value = 10000[tex]\frac{1-(1+0.0635)^{-7} }{0.0635}[/tex]

Present Value =10000[tex]\frac{0.35011}{0.0635}[/tex]

Present Value =10000 (5.5135978)

Present value= $ 55135.978

Which is the amount that must be paid at most to get annuities such that $10,000 annually over the 7-year period are to be received.

i will pick c put check it over to be sure

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3