Question

Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.

Answer 1

Every year, Sam will have 103% of the amount from the previous year.

`p\%=(p)/(100)\\\\103\%=(103)/(100)=1.03`

After the first year:

`1.03\cdot\$4,500`

After the second year:

`1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2`

After the t-th year:

`\$4,500(1.03)^t`

Therefore we have the inequality:

`\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^(15)\approx15.56\\\\\text{therefore}\ t\leq15`

Answer: t ≤ 15.