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
To calculate the compound interest, we'll use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment including interest
P = the principal investment amount (the initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
In this case, P = $100, r = 5% (or 0.05), n = 12, and t = 10. Plugging in these values into the formula:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 15528.234658...
Rounding this to the nearest place value, we get A ≈ 15528.23.
Now, we need to express the amount $15528.23 in the form of a × 10^n where a is a single digit.
To do this, we move the decimal point one place to the left, which gives us 1.5528234... Then, we multiply it by 10^4 to obtain 15.528234... Since the question asks for a single digit for a, we round it to 16.
Therefore, $15,528.23 can be expressed as 16 × 10^3.
it says wrong
Apologies for the error. Let's calculate it again.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment including interest
P = the principal investment amount (the initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years
P = $100, r = 5% (or 0.05), n = 12, and t = 10. Plugging in these values into the formula:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 1647.0090674374...
Rounding this to the nearest place value, we get A ≈ 1647.01
Now, we need to express the amount $1647.01 in the form of a × 10^n where a is a single digit.
To do this, we move the decimal point one place to the left, which gives us 16.4701. Then, we multiply it by 10^2 to obtain 1647.01.
Therefore, $1,647.01 can be expressed as 1.64701 × 10^3.