it takes 10 years for a 100$ monthly bank to deposit to a amount to $15,528.23 when invested at 5% interest compouneded monthly. round to the nearest place value, then express the amount $15,528.23 in the form of a x 10^n where is a single digit.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $100, the annual interest rate (r) is 5% (or 0.05 as a decimal), the number of times interest is compounded per year (n) is 12 (monthly compounding), and the number of years (t) is 10.
Using the formula:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1.004167)^120
A ≈ 100(1.647009)
A ≈ 164.7009
Rounding to the nearest cent, the amount in the account after 10 years would be approximately $164.70.
To express $15,528.23 in the form a × 10^n, we need to determine the appropriate value for a (a single digit) and n (the exponent). The number provided is already in decimal form.
Therefore, $15,528.23 can be written as 1.552823 × 10^4.
To solve this problem, we can use the formula for compound interest compounded monthly:
A = P(1 + r/n)^(nt)
where:
A = the amount after time t
P = the principal (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = $100 (monthly deposit)
r = 5% = 0.05 (annual interest rate in decimal form)
n = 12 (compounded monthly)
t = 10 years
First, we need to find the total amount of money deposited over the 10-year period. Since $100 is deposited monthly, the total amount deposited would be:
Total Deposits = monthly deposit * number of months = $100 * 12 months * 10 years = $12,000
Now, we can calculate the final amount using the compound interest formula:
A = P(1 + r/n)^(nt)
A = $12,000(1 + 0.05/12)^(12*10)
A ≈ $15,528.23
Thus, the amount after 10 years of compounding interest is approximately $15,528.23.
To express $15,528.23 in the form of a × 10^n, we shift the decimal point until there is only one digit to the left of it. In this case, we need to move the decimal point three places to the left to get 1.552823. Therefore, we can write:
$15,528.23 ≈ 1.552823 × 10^4
To find the amount in the account after 10 years of monthly deposits, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the amount deposited each month ($100)
r = the annual interest rate (5% or 0.05)
n = the number of times the interest is compounded per year (12 for monthly)
t = the number of years (10)
Plugging in the values, we get:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1.00416666667)^(120)
A ≈ 100(1.647009)
A ≈ $16,470.09
Rounding this to the nearest cent, we get $16,470.10.
To express $16,470.10 in the form a x 10^n, we need to move the decimal point so that there is only one non-zero digit to the left of it:
$16,470.10 = 1.64701 x 10^4
Therefore, the amount $15,528.23 in the requested form is approximately 1.647 x 10^4.