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
×
10
where a
is single digit.(1 point)
The formula to calculate the future value of an investment with compound interest is:
A = P(1 + r/n)^(nt)
where:
A is the future value
P is the principal amount ($100 monthly deposit)
r is the annual interest rate (5% or 0.05)
n is the number of times the interest is compounded per year (12 for monthly)
t is the number of years the money is invested (10 years)
We can plug in the values and solve for A:
A = 100(1 + 0.05/12)^(12*10)
A = $15,528.23
Now, we need to express $15,528.23 in the form of a×10^n where a is a single digit and n is the exponent.
$15,528.23 can be expressed as 1.552823 × 10^4
Therefore, the amount $15,528.23 can be expressed as a×10^n where a is 1.552823 and n is 4.