In 2012 the maximum Social Security deposit by an individual was $8,386.75. Suppose you are 33 and make a deposit of this amount into an account at the end of each year. How much would you have (to the nearest dollar) when you retire if the account pays 2% compounded annually and you retire at age 65?
Amount = 8386.75( 1.02^32 - 1)/.02
= ....
Thank you!
To calculate the amount you would have when you retire, you need to use the formula for compound interest. This formula is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment (amount you would have when you retire)
P = the principal amount (the initial deposit)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
Let's break down the problem:
Principal amount (P) = $8,386.75
Annual interest rate (r) = 2% = 0.02 (expressed as a decimal)
Number of times interest is compounded per year (n) = 1 (compounded annually)
Number of years (t) = 65 - 33 = 32 (years until retirement)
Now, let's substitute the values into the formula:
A = $8,386.75(1 + 0.02/1)^(1*32)
Simplifying the expression inside the parentheses:
A = $8,386.75(1.02)^32
Now, calculate this using a calculator or a spreadsheet:
A ≈ $14,446.88
So, you would have approximately $14,446.88 (to the nearest dollar) when you retire.