The problem has two parts. (a) Calculate the annual property tax and quarterly property tax for a property with an annual assessed value of $160,000$ and a property tax rate of $7\%$. (b) Saman borrowed $30,000$ at a simple interest rate and paid back $51,600$ after 3 years. Find the annual simple interest rate.

1. Problem Description

The problem has two parts.

(a) Calculate the annual property tax and quarterly property tax for a property with an annual assessed value of $160,000$ and a property tax rate of $7\%$.

(b) Saman borrowed $30,000$ at a simple interest rate and paid back $51,600$ after 3 years. Find the annual simple interest rate.

2. Solution Steps

(a)

First, calculate the annual property tax.

Annual property tax = Annual assessed value * Property tax rate

Annual property tax $= 160000 \times \frac{7}{100} = 11200$

Next, calculate the quarterly property tax. Since there are 4 quarters in a year,

Quarterly property tax = Annual property tax / 4

Quarterly property tax $= \frac{11200}{4} = 2800$

(b)

Let $P$ be the principal amount, $r$ be the annual simple interest rate, $t$ be the time in years, and $A$ be the total amount after $t$ years.

$P = 30000$

$A = 51600$

$t = 3$

The formula for simple interest is:

$A = P(1 + rt)$

$51600 = 30000(1 + 3r)$

$\frac{51600}{30000} = 1 + 3r$

$1.72 = 1 + 3r$

$3r = 1.72 - 1$

$3r = 0.72$

$r = \frac{0.72}{3} = 0.24$

The annual simple interest rate is $0.24$, or $24\%$.

3. Final Answer

(a) The annual property tax is $11,200$, and the quarterly property tax is $2,800$.

(b) The annual simple interest rate is $24\%$.