Question

It takes 10 years for $100 a monthly bank deposit to amount to $15,528.23 when invested at 5% interest composed monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a * 10^n where a is a single digit.

Answer 1

To express the amount $15,528.23 in the form of \( a \times 10^n \), where \( a \) is a single digit, we first need to convert \( 15,528.23 \) into that format.

1. Identify \( a \) and \( n \):
- We start by expressing \( 15,528.23 \) in scientific notation. We need to find \( a \) as a single digit and \( n \) as an exponent of 10.

2. Move the decimal point to create a number between 1 and 10:
- Shifting the decimal point 1 position to the left gives us:
\[
1.552823
\]
- This shows that \( a = 1.552823 \).

3. The corresponding exponent \( n \) becomes:
- Since we moved the decimal point one position to the left from \( 15,528.23 \), we have:
\[
n = 4
\]

4. Now, we ensure \( a \) is a single digit:
- We want to express it also in a form that \( a \) is truly a single digit. To do this, we can round:
\[
a = 1.6 \quad (when \, rounded)
\]

5. Therefore, combining these gives us:
\[
15,528.23 \approx 1.6 \times 10^4
\]

Thus, the value of \( 15,528.23 \) in the form of \( a \times 10^n \) is \( \boxed{1.6 \times 10^4} \).