I can not figure these out for the life of me. Any help is appreciated.
1. Find the final amount of an investment if $2,000 is invested at an interest rate of 8% compounded quarterly for 8 years.
I used interest formula and came up with $1,769.08.
And then:
I = .08/4 = .02
N = 8(4) = 32
Amount= 2,000(.02)^32
= 8.59 ?
And then:
2000(1+0.08/4)^4 = 2164.86
2. Find the possible values for a, if the distance between the points is 17 and the coordinates of the points are (-4, a) and (4, 2)
D= √(4 - (-4))^2 + (2 - a)^2
I used the distance formula and it came out as an imaginary number..
I = .08/4 = .02
N = 8(4) = 32
Amount= 2,000(.02)^32 ****NO****
Amount = 2,000(1.02)^32
= 3769.08
If you add 2% at every stage you multiply by 1.02 at every stage.
d^2 = 17^2 = 289
289 = 8^2 + (2-a)^2
289 = 64 + 4 - 4a + a^2
a^2 - 4 a -221 = 0
(a-17)(t+13) = 0
a = 17 or a = -13
Thank you very much, I was beyond stumped.
1. To find the final amount of an investment with compound interest, you can use the formula:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, you have:
P = $2,000
r = 8% = 0.08 (in decimal form)
n = 4 (quarterly compounding)
t = 8 years
Substituting these values into the formula, you get:
A = 2000(1 + 0.08/4)^(4*8)
Now let's calculate it step by step:
A = 2000(1 + 0.02)^(32)
A = 2000(1.02)^32
A ≈ 2000 * 1.902393
A ≈ $3,804.79
So, the final amount of the investment after 8 years would be approximately $3,804.79.
Your initial calculation of $1,769.08 seems to be incorrect. The correct answer is closer to $3,804.79.
2. To find the possible values of 'a' given that the distance between the points (-4, a) and (4, 2) is 17, you can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, you have:
(x1, y1) = (-4, a)
(x2, y2) = (4, 2)
d = 17
Substituting these values into the distance formula, you get:
17 = √((4 - (-4))^2 + (2 - a)^2)
Simplifying this equation, we have:
17 = √(8^2 + (2 - a)^2)
Squaring both sides to eliminate the square root, we get:
289 = 64 + (2 - a)^2
Rearranging and simplifying further:
289 - 64 = (2 - a)^2
225 = (2 - a)^2
Taking the square root of both sides to solve for 'a', we have:
±15 = 2 - a
Now, isolate 'a' by subtracting 2 from both sides:
±15 - 2 = -a
±13 = -a
To obtain the possible values for 'a', multiply both sides by -1:
a = ±13
Therefore, the possible values for 'a' that satisfy the distance between the points (-4, a) and (4, 2) being 17 are +13 and -13.