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×10n
where a
is single digit.(1 point)
To find the value of the monthly bank deposit after 10 years at a 5% interest rate compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (the monthly deposit)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
A = $15,528.23
P = $100
r = 5% = 0.05 (decimal form)
n = 12 (monthly compounding)
t = 10 years
Plugging in the values, we can solve for A:
$15,528.23 = $100(1 + 0.05/12)^(12*10)
Now, let me calculate it for you.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, P = $100, r = 5% = 0.05, n = 12 (monthly compounding), and t = 10 years. We need to solve for A.
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1.0041667)^(120)
A ≈ 100(1.647009)
A ≈ $164.70
Rounding to the nearest place value, the amount is $164.70.
To express $15,528.23 in the form of a×10^n, we need to find a and n in the equation A = a×10^n.
To do this, we can divide $15,528.23 by $164.70:
15,528.23 / 164.70 ≈ 94.21
This means, $15,528.23 is approximately 94.21 × $164.70.
Therefore, $15,528.23 can be expressed as 94.21×10^2.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A = the final amount after t years
P = the principal (monthly deposit)
r = the annual interest rate (in decimal form)
n = the number of times interest is compounded per year
t = the number of years
In this case, the monthly deposit is $100, the annual interest rate is 5% (or 0.05), and interest is compounded monthly (n = 12).
So, the formula becomes:
A = 100(1 + 0.05/12)^(12*10)
Now, we can calculate A:
A = 100(1 + 0.05/12)^(12*10)
A = 100(1.00416666667)^(120)
A = 100(1.647009)
A ≈ 16,470.09
Rounding to the nearest place value, $15,528.23 becomes $15,470.
To express $15,470 in the form of a×10^n, we need to write it as a number between 1 and 10 multiplied by a power of 10.
Dividing $15,470 by 10, we get:
15,470 ÷ 10 = 1,547.
So, we can express $15,470 as:
1.547 × 10^4.