Final answer:
We calculate the time until you have $168,000 by using the compound interest formula and adding the initial 2-year waiting period to the result.
Step-by-step explanation:
To determine how long you will wait from now until you have $168,000, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Since you plan to wait two years before investing the $33,000 you expect to receive, we need to find the time t such that $33,000 grows to $168,000 at a compound interest rate of 9.75% annually. Assuming that the interest is compounded annually (n = 1), the formula becomes 168000 = 33000(1 + 0.0975)^t. To solve for t, we would take the logarithm of both sides and isolate t.
To find the total number of years from now until you have $168,000, we need to add the 2-year waiting period to the time calculated using the compound interest formula.