To find the value of a and n, we will use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the amount after time t
P = the principal (monthly deposit)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, we have:
P = $100
r = 5% = 0.05 (as a decimal)
n = 12 (monthly compounding)
t = 10 years
Using the formula, we can solve for A:
A = P(1 + r/n)^(nt)
A = $100(1 + 0.05/12)^(12*10)
A = $100(1 + 0.0041667)^(120)
A = $100(1.0041667)^(120)
A ≈ $15,528.23
So, the amount after 10 years is approximately $15,528.23.
Now, let's express this amount in the form of a×10^n. Rounding to the nearest place value gives us:
$15,528.23 ≈ $15,500
The value of a is 1 (as the first digit in $15,500) and n is 4 (as the number of decimal places added when expressing $15,500 in scientific notation as a×10^n).
Therefore, $15,528.23 can be expressed as 1×10^4.
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×10n
where a
is single digit
1 answer