To determine how much money you should put in the savings account now to ensure your child has $10,000 in 10 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)
Using this formula, we can solve for P, the amount of money we need to put in the account now:
A = $10,000 (the future value we want)
r = 0.05 (the annual interest rate)
n = 1 (since interest is compounded annually)
t = 10 (the time period in years)
P = A / (1 + r/n)^(nt)
P = $10,000 / (1 + 0.05/1)^(1*10)
P = $10,000 / (1.05)^10
P = $10,000 / 1.62889
Therefore, you should put approximately $6,131.41 in the savings account now to ensure that you will have $10,000 in 10 years, assuming a 5% annual interest rate compounded annually.