it takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% intrest compounded monthly. round to the nearest place value, then express the amount $15,528.23 in the form of ax10^n where a is sungle digit
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 (monthly deposit)
r = the annual interest rate (converted to decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal amount is $100, the annual interest rate is 5% (0.05 as a decimal), the interest is compounded monthly, and the time is 10 years.
A = 100(1 + 0.05/12)^(12*10)
Now we can calculate the future value:
A ≈ 100(1 + 0.0041666666666667)^(120)
A ≈ 100(1.0041666666666667)^120
A ≈ 100(1.647009)
A ≈ 164.7009
Rounded to the nearest place value, the amount is $164.70.
To express $15,528.23 in the form of ax10^n, we can use scientific notation. In this case, the nearest single-digit number to $15,528.23 is 2. Therefore:
$15,528.23 ≈ 2x10^4