Robin, who is self-employed, contributes $5500/year into a Keogh account. How much will he have in the account after 35 years if the account earns interest at the rate of 2.5%/year compounded yearly? (Round your answer to the nearest cent.)
To calculate the future value of Robin's Keogh account after 35 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the principal investment (in this case, Robin's annual contribution of $5500)
r = the annual interest rate (in decimal form: 2.5% = 0.025)
n = the number of times interest is compounded per year (in this case, yearly)
t = the number of years (in this case, 35)
Substituting the given values into the formula:
A = 5500(1 + 0.025/1)^(1*35)
Calculating inside the parentheses:
A = 5500(1 + 0.025)^(35)
Calculating the exponent:
A = 5500(1.025)^35
Calculating (1.025)^35:
A ≈ 5500(1.94061667)
Calculating the final value:
A ≈ $10,673.39
Therefore, Robin will have approximately $10,673.39 in the Keogh account after 35 years.
To find out how much Robin will have in the Keogh account after 35 years with the given interest rate, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount in the account
P = the principal amount (initial contribution)
r = annual interest rate (as a decimal)
n = number of times interest is compounded per year
t = number of years
In this case, Robin contributes $5500 each year, so the initial contribution is P = $5500. The interest rate is given as 2.5%, or r = 0.025 as a decimal. The interest is compounded yearly, so n = 1. And the time period is 35 years, so t = 35.
Substituting these values into the formula, we have:
A = 5500(1 + 0.025/1)^(1*35)
A = 5500(1 + 0.025)^(35)
A ≈ 5500(1.025)^35
Calculating this using a calculator or spreadsheet, we find that A ≈ $14,821.34. Therefore, Robin will have approximately $14,821.34 in the Keogh account after 35 years.
Assuming the payments are made at the end of the year, that way the formula fits,
amount = 5500( 1.025^35 - 1) / .025
= ....
If you don't get around $300,000 let me know so we can find out where you are going wrong.