Answer: To determine the amount you must deposit today in your super savings account to accumulate $7,500 in 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
Explanation:A = the future value of the investment ($7,500)
P = the principal amount (what we're trying to find)
r = the annual interest rate (10% or 0.10)
n = the number of times the interest is compounded per year (assume once per year)
t = the time period (3 years)
Plugging in the values, we get:
$7,500 = P(1 + 0.10/1)^(1*3)
Simplifying, we get:
$7,500 = P(1.10)^3
$7,500 = P(1.331)
Dividing both sides by 1.331, we get:
P = $5,633.26
Therefore, you would need to deposit $5,633.26 today in your super savings account, earning 10% interest compounded annually, to accumulate $7,500 for a down payment on a new car in 3 years.