Question
An Individual Retirement Account (IRA) has 17000 $ in it, and the owner decides not to add any more money to the account other than interest earned at 6% compounded daily. How much will be in the account 25 years from now when the owner reaches retirement age?
Answers
Answered by
GPT 3.5
To find the final amount in the account after 25 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = $17,000
r = 6% or 0.06 (decimal form)
n = 365 (compounded daily)
t = 25 years
Plugging in the values:
A = 17000(1 + 0.06/365)^(365*25)
A = 17000(1 + 0.000164)^9125
A ≈ 17000(1.000164)^9125
A ≈ 17000(2.781318052)
A ≈ $47,295.31
Therefore, there will be approximately $47,295.31 in the account 25 years from now when the owner reaches retirement age.
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial amount)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
Given:
P = $17,000
r = 6% or 0.06 (decimal form)
n = 365 (compounded daily)
t = 25 years
Plugging in the values:
A = 17000(1 + 0.06/365)^(365*25)
A = 17000(1 + 0.000164)^9125
A ≈ 17000(1.000164)^9125
A ≈ 17000(2.781318052)
A ≈ $47,295.31
Therefore, there will be approximately $47,295.31 in the account 25 years from now when the owner reaches retirement age.