It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a×10^n
where a is single digit.
It's 2x10^4
To find the amount in the form of a×10^n, we need to round the given value, $15,528.23, to the nearest place value.
Rounding $15,528.23 to the nearest dollar, the value becomes $15,528.
Now, we need to express this value in the form of a×10^n, where a is a single digit.
The value $15,528 can be written as 1.5528 × 10^4.
Therefore, in the form of a×10^n, $15,528.23 is approximately 1.5528 × 10^4.
To solve this problem, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (in this case, $15,528.23)
P = the initial deposit (in this case, $100)
r = the annual interest rate (5%)
n = the number of times interest is compounded per year (12, since it's compounded monthly)
t = the number of years (10)
Now we can substitute these values into the formula:
$15,528.23 = $100(1 + 0.05/12)^(12*10)
To solve for the exponential part, we simplify the fraction:
$15,528.23 = $100(1 + 0.00417)^(120)
Calculating the exponential:
$15,528.23 = $100(1.00417)^(120)
Now we can solve for the value inside the parentheses:
(1.00417)^(120) = 15,528.23 / 100
(1.00417)^(120) ≈ 155.2823
Now we need to express $15,528.23 in the form of a×10^n. We'll round to the nearest place value:
Rounding to the nearest place value, $15,528.23 becomes $15,528.00.
To express this in the form of a×10^n, we need to move the decimal point to the right until we have a single digit to the left of the decimal point:
$15,528.00 = $1.552800 × 10^4
Thus, the amount $15,528.23 is approximately $1.552800 × 10^4 in the form of a×10^n.
sorry you're incorrect.
I apologize for the error. Let's redo the calculation.
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount ($15,528.23)
P = the initial deposit ($100)
r = the annual interest rate (5% or 0.05 as a decimal)
n = the number of times interest is compounded per year (12, for monthly compounding)
t = the number of years (10)
Plugging in the values into the formula, we have:
$15,528.23 = $100(1 + 0.05/12)^(12*10)
$15,528.23 = $100(1 + 0.004167)^(120)
To solve for (1 + 0.004167)^(120), we can divide both sides by $100:
155.2823 = (1 + 0.004167)^(120)
Now, let's express 155.2823 in the form a×10^n.
155.2823 ≈ 1.552823 × 10^2
(rounded to two decimal places, as specified in the problem)
Therefore, the amount $15,528.23 is approximately $1.552823 × 10^4 in the form of a×10^n.
Remember it say a is single digit.
I apologize for forgetting the requirement that a must be a single digit.
To express the amount $15,528.23 in the form of a×10^n, where a is a single digit, we need to adjust the value by moving the decimal point.
Since $15,528.23 is already in the correct form as a decimal, we can simply move the decimal point to the left until we have a single digit to the left of the decimal point:
$15,528.23 ≈ $1.552823 × 10^4
Therefore, the amount $15,528.23 can be expressed in the form of a×10^n as $1.552823 × 10^4.
Thanks for trying.
You're welcome. I apologize for the confusion and any inconvenience caused. If you have any other questions, please feel free to ask.
My apologies for misunderstanding your requirement earlier. You are correct.
To express the amount $15,528.23 in the form of a×10^n, where a is a single digit and after rounding, the answer is indeed 2×10^4.
Thank you for clarifying, and I apologize for any confusion caused.