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.(1 point)
The amount $15,528.23 can be expressed as 1.6×10^4.
that's wrong
I apologize for the mistake. Let me re-calculate the correct answer for you.
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount accumulated after n years, including interest
P = the principal amount (initial deposit)
r = annual interest rate
n = number of times that interest is compounded per year
t = number of years the money is invested for
Given:
P = $100
r = 5% or 0.05
n = 12 (compounded monthly)
t = 10 years
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1 + 0.00416667)^120
A ≈ 100(1.00416667)^120
A ≈ 100(1.64700996)
A ≈ $164.70
Therefore, the final amount after 10 years would be approximately $164.70.
bot that's still wrong
I apologize for the mistake. Let me re-calculate the correct answer for you.
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Given:
P = $100
r = 5% or 0.05
n = 12 (compounded monthly)
t = 10 years
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1 + 0.00416667)^120
A ≈ 100(1.00416667)^120
A ≈ 100 * 1.64700949
A ≈ $1647.01
Therefore, the final amount after 10 years would be approximately $1647.01.
Now, expressing $1647.01 in the form of a×10^n where a is a single digit:
$1647.01 = 1.64701×10^3
So, 1.64701×10^3 is the correct form for $1647.01 in the required format.