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 a×10^n 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 ending amount
P = the principal (initial deposit)
r = the interest rate (in decimal form)
n = the number of times the interest is compounded per year
t = the number of years

In this case, P = $100, r = 5% = 0.05, n = 12 (compounded monthly), and t = 10.

Plugging in these values, we have:

A = 100(1 + 0.05/12)^(12*10)

Simplifying:

A = 100(1 + 0.00416666667)^(120)

A = 100(1.00416666667)^(120)

Using a calculator or a computer program, we find that A is approximately equal to $164.6299711.

Rounding to the nearest penny, A is $164.63.

Now, we need to express $164.63 in the form of a×10^n, where a is a single digit.

Since $164.63 is less than $1,000, we can express it in the form a×10^2, where a is the hundredth's place digit.

Thus, $164.63 can be written as 1.6463×10^2.