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 of monthly deposits, we can use the formula for compound interest:

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

Where:
A = the amount of money accumulated after time t
P = the initial deposit
r = the annual interest rate (in decimal form)
n = the number of times that interest is compounded per year
t = the number of years

In this case, the initial deposit is $100, the annual interest rate is 5% (or 0.05 in decimal form), and the interest is compounded monthly (so n = 12).

Using the given information, we have:

A = $100(1 + 0.05/12)^(12*10)
A = $100(1.00416666667)^(120)
A = $100(1.647009483)
A ≈ $164.70

Therefore, the amount after 10 years of monthly deposits is approximately $164.70 when rounded to the nearest cent.

To express this amount in the form a×10^n, we can convert it to scientific notation:

A = 1.647 × 10^2

Therefore, the amount $164.70 can be expressed in the form a×10^n as 1.647 × 10^2.