If a merchant deposits $1,500 annually at the end of each tax year in an IRA account paying interest at the rate of 10%/year compounded annually, how much will she have in her account at the end of 25 years? Round your answer to two decimal places
16,252.06
To calculate the future value of the IRA account at the end of 25 years, we can use the formula for compound interest:
Future Value = Principal × (1 + interest rate)^number of periods
In this case, the annual deposit of $1,500 is the principal, the interest rate is 10% (or 0.10), and the number of periods is 25 years.
Since the deposit is made at the end of each year, we can consider it as an ordinary annuity. To calculate the future value of an ordinary annuity, we can use the following formula:
Future Value = (Deposit × ((1 + interest rate)^number of periods - 1)) / interest rate
Let's calculate the future value:
Future Value = (1500 × ((1 + 0.10)^25 - 1)) / 0.10
= (1500 × (1.10^25 - 1)) / 0.10
= (1500 × (10.835 - 1)) / 0.10
= (1500 × 9.835) / 0.10
= 14752.50
Therefore, the merchant will have approximately $14,752.50 in her account at the end of 25 years.
To find the amount in the IRA account at the end of 25 years, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value or final amount
P = the principal amount (initial deposit)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $1,500 (annual deposit)
r = 10% = 0.10 (interest rate)
n = 1 (compounded annually)
t = 25 (number of years)
Plug in these values into the formula:
A = $1,500(1 + 0.10/1)^(1*25)
First, simplify the part inside the parentheses:
A = $1,500(1 + 0.10)^(25)
Then, calculate the total value:
A = $1,500 * (1.10)^25
Using a calculator, raise 1.10 to the power of 25:
A ≈ $15,522.45
Therefore, the merchant will have approximately $15,522.45 in her IRA account at the end of 25 years.