Suppose $1.00 amounts to 1.082431 at 8% compounded quarterly. How much does
$200 amount to?
(a) $ 126.82 (b) $ 101.46 (c) $ 216.49 (d) $ 380.47 (e) $ 250.00
A = 200 * 1.082431 = $216.49.
To find out how much $200 will amount to, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial amount)
r = the interest rate (in decimal form)
n = the number of times compounded per year
t = the number of years
Given:
P = $200
r = 8% = 0.08 (converted to decimal form)
n = 4 (quarterly compounding)
t = 1 (one year)
Substituting these values into the formula, we get:
A = $200(1 + 0.08/4)^(4*1)
A = $200(1.02)^4
A ≈ $200(1.08243)
To find the final amount, we multiply the principal amount by (1.08243):
A ≈ $200 * 1.08243
A ≈ $216.49
Therefore, $200 will amount to approximately $216.49.
So the answer is (c) $216.49.
To find out how much $200 amounts to at 8% compounded quarterly, we can use the compound interest formula:
A = P(1 + r/n)^(n*t)
Where:
A = the future value of the investment
P = the principal amount ($200 in this case)
r = the annual interest rate (8% or 0.08 in decimal form)
n = the number of times the interest is compounded per year (quarterly in this case, so n = 4)
t = the number of years
Plugging in the values:
A = 200(1 + 0.08/4)^(4*t)
To find the value of A, we need to determine the value of t. Since the original amount of $1.00 amounts to 1.082431, we can determine the value of t using the following equation:
1.082431 = (1 + 0.08/4)^(4*t)
We can solve this equation to find the value of t. Taking the natural logarithm (ln) of both sides gives:
ln(1.082431) = ln((1 + 0.08/4)^(4*t))
Using the power rule of logarithms, we can move the exponent down:
ln(1.082431) = (4*t) * ln(1 + 0.08/4)
Now, we can solve for t:
t = [ln(1.082431)] / [4 * ln(1 + 0.08/4)]
After finding the value of t, we can use it to calculate the future value of $200:
A = 200(1 + 0.08/4)^(4*t)
Calculating this expression will give us the answer in dollars.