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Ivenika [448]
3 years ago
7

Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the num

ber of years, t, for which the account will have less than or equal to $7,020.
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
3 0

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

p\%=\dfrac{p}{100}\\\\103\%=\dfrac{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

<h3>Answer: t ≤ 15.</h3>
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