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

1 answer

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 amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

In this case, the principal amount (P) is $100, the annual interest rate (r) is 5% (or 0.05 as a decimal), the number of times interest is compounded per year (n) is 12 (monthly compounding), and the number of years (t) is 10.

Using the formula:

A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1.004167)^120
A ≈ 100(1.647009)
A ≈ 164.7009

Rounding to the nearest cent, the amount in the account after 10 years would be approximately $164.70.

To express $15,528.23 in the form a × 10^n, we need to determine the appropriate value for a (a single digit) and n (the exponent). The number provided is already in decimal form.

Therefore, $15,528.23 can be written as 1.552823 × 10^4.