Question

sally’s parents deposited $15,000 into a college savings account on her third birthday. the account had an interest rate of 9.6% compounded annually. they were hoping that the money would double twice by the time she was 18 years old. using the rule of 72, $t = \frac{72}{r}$, will their hopes come true? \bigcirc yes, the $15,000 will double each 7.5 years. in 15 years, it will double twice. \bigcirc yes, the $15,000 will double in 7.5 years and be four times as much in 15 years. \bigcirc no, the $15,000 will only double once in 15 years, not double twice. \bigcirc no, it will take 30 years for the $15,000 to double twice.

Explanation:

Step1: Calculate doubling time

Use Rule of 72: $t = \frac{72}{r} = \frac{72}{9.6} = 7.5$ years.

Step2: Find time period

Time from 3 to 18: $18 - 3 = 15$ years.

Step3: Check doubling count

Number of doublings: $\frac{15}{7.5} = 2$. Doubling twice means 4x original amount.

Answer:

A. Yes, the $15,000 will double each 7.5 years. In 15 years, it will double twice., B. Yes, the $15,000 will double in 7.5 years and be four times as much in 15 years.