Question
It takes 10 years for $100 monthly bank deposit to amount to 15,528.23 when invested at 5% interest compounded monthly around to the nearest place value then express the amount $15,528.23 in the form of a times x 10 to the power of where a is a symptom
Answers
Answered by
GPT 3.5
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt),
where:
A = the final amount (15,528.23)
P = the principal (monthly deposit) ($100)
r = annual interest rate (5% or 0.05)
n = number of times interest is compounded per year (12 because it is compounded monthly)
t = number of years (10)
Substituting the given values into the formula and solving for A:
15,528.23 = 100(1 + 0.05/12)^(12*10)
15,528.23 = 100(1.0041666666666666666666666666667)^(120)
15,528.23 = 100(1.6470096119105817001165409070191)
15,528.23 = 164.70096119105817001165409070191
Therefore, rounding to the nearest place value, the amount is approximately $164.70.
To express 15,528.23 in the form of a × 10^b, we move the decimal point in 15,528.23 until there is only one digit to the left of the decimal point:
1.552823 × 10^4.
Now, let's answer the final part of the question. The mention of "a symptom" seems unrelated to the problem, so we cannot provide any interpretation for that.
A = P(1 + r/n)^(nt),
where:
A = the final amount (15,528.23)
P = the principal (monthly deposit) ($100)
r = annual interest rate (5% or 0.05)
n = number of times interest is compounded per year (12 because it is compounded monthly)
t = number of years (10)
Substituting the given values into the formula and solving for A:
15,528.23 = 100(1 + 0.05/12)^(12*10)
15,528.23 = 100(1.0041666666666666666666666666667)^(120)
15,528.23 = 100(1.6470096119105817001165409070191)
15,528.23 = 164.70096119105817001165409070191
Therefore, rounding to the nearest place value, the amount is approximately $164.70.
To express 15,528.23 in the form of a × 10^b, we move the decimal point in 15,528.23 until there is only one digit to the left of the decimal point:
1.552823 × 10^4.
Now, let's answer the final part of the question. The mention of "a symptom" seems unrelated to the problem, so we cannot provide any interpretation for that.