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)

Answer 1

The amount $15,528.23 can be expressed as 1.6×10^4.

Answer 2

that's wrong

Answer 3

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.

Answer 4

bot that's still wrong

Answer 5

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.