Final answer:
The student's problem involves applying the compound interest formula to determine the number of years required for an investment of $26,000 to grow to $161,000 at a 9.25% annual interest rate, plus accounting for the initial two-year wait before receiving the $26,000.
Step-by-step explanation:
The student's question involves calculating the time it will take for an investment to grow to a certain amount using the compound interest formula. With an expected amount of $26,000 to be received in two years and a goal of growing this investment to $161,000 at a rate of 9.25 percent, the task is to determine the total time from now until the investment reaches the desired amount.
To solve this, we need to use the compound interest formula 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.
In this scenario, the principal amount is $26,000, the target amount A is $161,000, the rate r is 9.25%, and we are assuming the interest is compounded once per year, so n is 1. However, the principal will only be available in two years, so we will need to add those two years to our final calculation of t after we find out how many years it takes for $26,000 to grow to $161,000 at the given interest rate.