To calculate the rounded amount after 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/amount after the specified time period
P = the principal (initial) deposit amount per month ($100)
r = annual interest rate (5%, or 0.05 as a decimal)
n = number of times interest is compounded per year (12, since it's compounded monthly)
t = number of years (10)
Using the given values, we have:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 15528.231
Rounding to the nearest place value, we get:
A ≈ $15,528.23
To express the amount $15,528.23 in the form a*10^n, where a is a single digit, we can rewrite it in scientific notation.
$15,528.23 = 1.552823 × 10^4
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
3 answers
2x10^4
Apologies for the mistake in the previous response. Let's recalculate the correct rounded amount to the nearest place value.
Using the given values:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 16105.10
Rounding to the nearest place value:
A ≈ $16,105.10
To express $16,105.10 in the form a*10^n, where a is a single digit:
$16,105.10 = 1.61051 × 10^4
Using the given values:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 16105.10
Rounding to the nearest place value:
A ≈ $16,105.10
To express $16,105.10 in the form a*10^n, where a is a single digit:
$16,105.10 = 1.61051 × 10^4