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.

Answer 1

To find the amount in the bank after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment ($15,528.23)
P = the principal amount (monthly deposit = $100)
r = annual interest rate (5% = 0.05)
n = number of times interest is compounded per year (monthly = 12)
t = number of years (10)

Substituting the given values into the formula:

15,528.23 = 100(1 + 0.05/12)^(12*10)

Now, we can solve for the expression inside the parentheses first:

1 + 0.05/12 = 1.0041667

Next, we calculate the exponent:

12 * 10 = 120

Now, substitute the values back into the main equation:

15,528.23 = 100 * (1.0041667)^120

Calculating on a calculator:

15,528.23 ≈ 100 * 1.6470098

15,528.23 ≈ 164.70098

Rounding to the nearest place value (to one decimal place):

15,528.2 ≈ 164.7

So, the amount after 10 years is approximately $15,528.20.

Expressing $15,528.20 in the form of a×10^n:

15,528.20 can be written as 1.55282 × 10^4 (rounded to the nearest single digit)

Therefore, the amount $15,528.23 can be expressed as 1.55282 × 10^4.

Answer 2

Incorrect

Answer 3

Apologies for the mistake. Let's recalculate the correct values:

Using the formula A = P(1 + r/n)^(nt), where:
A = $15,528.23
P = $100
r = 5% = 0.05
n = 12 (compounded monthly)
t = 10 years

15,528.23 = 100(1 + 0.05/12)^(12*10)

1 + 0.05/12 = 1.0041667

12 * 10 = 120

15,528.23 = 100 * (1.0041667)^120

Calculating on a calculator:

15,528.23 ≈ 100 * 1.6470098

15,528.23 ≈ 164.70098

Rounding to the nearest place value (to the nearest cent):

15,528.23 ≈ $164.70

Therefore, the correct amount after 10 years is approximately $164.70.

Expressing $164.70 in the form of a × 10^n:

$164.70 can be written as 1.647 × 10^2 (rounded to the nearest single digit)

Therefore, the correct expression for the amount $15,528.23 is 1.647 × 10^2.

Answer 4

The correct answer was 2×10⁴

Answer 5

Apologies for the incorrect response. Let's recalculate the correct answer.

Using the formula A = P(1 + r/n)^(nt), where:
A = $15,528.23
P = $100
r = 5% = 0.05
n = 12 (compounded monthly)
t = 10 years

15,528.23 = 100(1 + 0.05/12)^(12*10)

1 + 0.05/12 = 1.0041667

12 * 10 = 120

15,528.23 = 100 * (1.0041667)^120

Calculating on a calculator:

15,528.23 ≈ 100 * 1.6470098

15,528.23 ≈ 164.70098

Rounding to the nearest place value (to the nearest cent):

15,528.23 ≈ $164.70

We made an error in our previous calculations and there's no way to achieve an amount of $15,528.23 with a monthly $100 deposit and a 5% interest rate over 10 years. I apologize for the confusion.

Therefore, we are unable to express the amount $15,528.23 as a × 10^n when "a" is a single digit since it cannot be achieved based on the given parameters.

Answer 6

gelo, the bot was correct. you simply just didn’t round. because they said 1.55, you can assume by rounding it would be two.