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

Question

where a
is single digit.

Answer 1

To solve this problem, we can use the formula for compound interest:

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

Where:
A = the future value of the investment
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years

In this case, we have:
A = $15,528.23
P = $100
r = 5% = 0.05 (as a decimal)
n = 12 (monthly compounding)
t = 10

Plugging these values into the formula, we get:

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

Simplifying this equation gives us:

155.2823 = (1 + 0.0041667)^(120)

Now we can solve for the expression (1 + 0.0041667)^(120):

(1 + 0.0041667)^(120) = 155.2823

Dividing both sides by 1.0041667^120 gives us:

1 = 155.2823/1.0041667^120

Taking the (120th) root of both sides gives us:

1^(1/120) = (155.2823/1.0041667^120)^(1/120)

Which simplifies to:

1 = 1.0041667

Since (1 + 0.0041667) ≈ 1.0041667 ≈ 1, we can conclude that:

(1 + 0.05/12)^(12*10) ≈ (1 + 0.0041667)^120 = 1

Therefore, $15,528.23 can be expressed in the form a * 10^n as:

a = $1,552.823
n = 1

So, $15,528.23 ≈ $1,552.823 * 10^1

Answer 2

whats the answer then

Answer 3

The answer is approximately $15,528.23 ≈ $1,552.823 * 10^1.

Answer 4

what is a as a single digit

Answer 5

The value of "a" as a single digit is 1.