Use the formula y=a(1+ rn)^(nt). Note that we want to solve two inequalities, y≥ 1200 and y≥ 3500.
at least $1200: about 5.22 years. at least $3500: about 35.85 years.
Practice makes perfect
Since the interest is compounded monthly, we have to use a formula that describes compound interest.
y=a(1+r/n)^(nt)
In this function, a is the initial amount, r is the percent increase expressed in decimal form, t is the time in years and n is the number of times the initial principal is compounded per year. From the exercise, we know that a=1000, r= 0.035 and n= 12 since the interest is compounded monthly.
y=1000(1+0.035/12)^(12t)We want to know the value of t when y is greater than or equal to 1200. Let's first simplify as much as possible and isolate the term with the variable in the exponent.
