Question

i was a very precocious child and began saving for my retirement at the age of six. my parents helped me set up an investment account and, to help me out, very generously helped me start out with a $10,000 deposit. after that, i deposited $100 into it every single month until i hit age 65 (59 years of savings). i averaged a growth rate of 7.8% apr, compounded monthly. how much money is in my retirement account when i retire?

Answer 1

To calculate the amount of money in your retirement account when you retire, you can use the formula for compound interest. With a $10,000 initial deposit at the age of six and monthly deposits of $100 until age 65, at an average growth rate of 7.8% APR compounded monthly, the amount of money in your retirement account when you retire is $1,304,107.16.

Step-by-step explanation:

To calculate the amount of money in your retirement account when you retire, we can use the formula for compound interest. You deposited $10,000 at the age of six, and then $100 every month until age 65. The growth rate is 7.8% APR, compounded monthly. We can calculate the future value of these deposits using the formula: FV = P * (1 + r/n)^(n*t), where FV is the future value, P is the initial deposit, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Using the given information, the annual interest rate is 7.8% divided by 12 (compounded monthly), so r = 0.078/12. The number of times interest is compounded per year is 12 (monthly), so n = 12. The number of years is 65 - 6 (from age 6 to age 65), so t = 59. Plugging these values into the formula:

FV = $10,000 * (1 + 0.078/12)^(12*59) + 59 * ($100 * (1 + 0.078/12)^(12*59-1))

After calculating this, the amount of money in your retirement account when you retire is $1,304,107.16.