The time it will take to save $1550.00 with semi-annual deposits of $171.00 in an account with 11% interest compounded semi-annually cannot be found with a simple formula. A financial calculator or a spreadsheet is required to compute the number of periods, which can then be translated into years and months.
To determine how long it will take to save $1550.00 by making deposits of $171.00 at the end of every six months into an account earning 11% interest compounded semi-annually, we must calculate the future value of an annuity due to the regular deposits and the compounding interest.
The future value of an annuity formula for compound interest is:
FV = P * [((1 + r/n)^(nt) - 1) / (r/n)],
where:
FV = future value of the annuity,
P = periodic deposit amount,
r = annual interest rate (in decimal),
n = number of times the interest is compounded per year,
t = the number of years.
However, since a simple formula does not exist for solving for t when the future value, periodic deposit, interest rate, and number of periods are known, we must rely on a financial calculator, a spreadsheet, or iterative methods to find the amount of time.
Using either of those methods, you would input your parameters (P = 171, r = 0.11, n = 2, FV = 1550), and solve for t. The answer will be in the number of semi-annual periods which you would then translate into years and months by dividing by 2 (for the semi-annual periods per year) and then multiply the decimal by 12 to find the remaining months.