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?
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.
To calculate the future value of an IRA, we can use the formula for compound interest:
Future Value = Principal * (1 + (Interest Rate/Number of Compounding Periods)) ^ (Number of Compounding Periods * Time)
In this case, the principal amount is $17,000, the interest rate is 6% (or 0.06), and the number of compounding periods is 365 (since it is compounded daily). The time period is 25 years.
So, the formula becomes:
Future Value = $17,000 * (1 + (0.06/365)) ^ (365 * 25)
Calculating this, we get:
Future Value = $17,000 * (1 + 0.00016438) ^ 9,125
Using a calculator or any programming language, we find:
Future Value = $17,000 * 2.554928362
Thus, the future value of the IRA will be approximately $43,455.77.
To find the amount in the IRA after 25 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the initial principal amount ($17,000)
r = the annual interest rate (6% or 0.06 as a decimal)
n = the number of times interest is compounded per year (daily, so 365)
t = the number of years (25)
Now, let's plug in these values into the formula and calculate the future value:
A = 17000(1 + 0.06/365)^(365*25)
First, calculate the value inside the parentheses:
1 + 0.06/365 = 1.00016438356
Next, calculate the exponent:
365 * 25 = 9125
Now, substitute these values back into the formula:
A = 17000(1.00016438356)^9125
Using a calculator, evaluate the expression inside the parentheses and then multiply it by $17,000 to find the future value of the IRA after 25 years.