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/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested or the loan is outstanding
In this case, we are given:
P = $100 (monthly deposit)
r = 5% (annual interest rate, so 0.05 as a decimal)
n = 12 (compounded monthly)
t = 10 years
Using the formula, we can substitute these values and solve for A:
A = $100(1 + 0.05/12)^(12*10)
A ≈ $100 * (1 + 0.00416666667)^(120)
A ≈ $100 * (1.00416666667)^(120)
A ≈ $100 * 1.647009
A ≈ $164.70
However, the problem asks us to round to the nearest place value and express the answer in the form of "a×10n".
Rounding $164.70 to the nearest place value is $165.
Therefore, the amount after 10 years would be approximately $165.
We can express this in the form of "a×10n" as 1.65×10^2, where aa is the single digit.
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×10na×10n where aa is single digit.(1 point)
1 answer