How many years will it take 400 to grow to 1671 if it is invested at 10 percent compounded annually?

To determine how many years it will take for an investment of $400 to grow to $1671 at an annual interest rate of 10% compounded annually, you can use the formula for compound interest: ( A = P(1 + r)^t ), where ( A ) is the future value, ( P ) is the principal amount, ( r ) is the interest rate, and ( t ) is the number of years. Rearranging the formula to solve for ( t ), you get ( t = \frac{\log(A/P)}{\log(1 + r)} ). Plugging in the values gives ( t = \frac{\log(1671/400)}{\log(1.10)} ), which calculates to approximately 11.5 years. Thus, it will take about 12 years for the investment to grow to $1671.