safiya deposited money into a bank account that earned 6.5% simple interest each year. after 3 1/2 years…

safiya deposited money into a bank account that earned 6.5% simple interest each year. after 3 1/2 years, she had earned $36.40 in interest on the account. no other money was deposited into or withdrawn from the account. how much was her initial deposit? enter your answer in the box. $

safiya deposited money into a bank account that earned 6.5% simple interest each year. after 3 1/2 years, she had earned $36.40 in interest on the account. no other money was deposited into or withdrawn from the account. how much was her initial deposit? enter your answer in the box. $

Answer

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We are given that $I=$36.40$, $r = 6.5%=0.065$, and $t = 3.5$ years.

Step2: Solve for $P$

From $I = Prt$, we can isolate $P$ by dividing both sides of the equation by $rt$. So $P=\frac{I}{rt}$. Substitute the given values: $P=\frac{36.40}{0.065\times3.5}$. First, calculate $0.065\times3.5 = 0.2275$. Then, $P=\frac{36.40}{0.2275}=160$.

Answer:

$160$