Financial Literacy

Before we changing any numbers, let's use the simple interest formula to determine how much money Zosia earns on her deposit in the current situation. cl I= p r t, where & I =Interest & p& = Principal r& = Annual interest rate t& = Time (in years) We know that the principal is $ 2400, the annual interest rate is 2.2 %, and the time is 5 years. Let's use 2.2 % in decimal form, 0.022, to make our calculations easier. p= 2400, r= 0.022, t= 5 Let's now substitute these values into the simple interest formula and evaluate the right-hand side to calculate the amount of interest.

We found that the simple interest over 5 years is $ 264. Now we will calculate the interest for each option one at a time.

Increasing the Interest Rate by 1 %

Let's calculate simple interest for the same principal and time period but with a 1 % higher interest rate. We can write 1 % as a decimal as 0.01.

Let's substitute these values into the simple interest formula and evaluate the right-hand side.

We got that the simple interest over 5 years would be $ 384 if the rate is increased by 1 %. This means that the simple interest earned is $ 384 - $ 264, or $ 120, more if the rate is increased by 1 %. $ 384 - $ 264 = $120

Increasing the Time by 1 Year

This time we will determine what happens with the simple interest if the time is increased by 1 year.

Like we did before, we will substitute these values into the simple interest formula and evaluate the right-hand side.

This time, the simple interest is $ 316.80. Let's calculate the difference between the amount of simple interests. 316.80-264=52.80 The simple interest earned is $ 52.80 more if the time is increased by 1 year.

Conclusion

Let's summarize what we have in a table.

As we can see, Zosia can earn more interest if the annual interest rate is increased by 1 % than if she received an extra year of interest at the current rate.

We are asked to find what Zosia's mother will owe the second month if she only pays $ 52 the first month. We know that the first month she has the loan, she owes $ 4500. Then she pays $ 52 for her first payment. Let's calculate her unpaid balance after the first payment. $ 4500- $ 52= $ 4448 After the first payment, her principal unpaid balance is $ 4448. However, each month, 1 % of the unpaid balance is added to the amount she owes. If we add 1 % of $ 4448 to $ 4448, we will get the amount of money that she will owe the second month. Remember that 1 % = 0.01!

If she only pays $ 52 in the first month, she will owe $ 4492.48 in the second month.

Now we want to find what Zosia's mother will owe in the third month if she makes the minimum payment each month. From Part A, we know that if she pays $ 52 the first month, she will owe $ 4492.48 the second month. Let's calculate her unpaid balance after the second payment. $ 4492.48- $ 52= $ 4440.48 After the second payment, her unpaid balance is $ 4440.48. Now let's calculate and add the 1 % interest of this amount to find her total balance, the same way we did in Part A. This will give us her balance going into the third month. Let's do it!

We found that Zosia's mother will owe about $ 4484.88 going into the third month.

We want to find the final price of the drone. We will start by calculating the dollar amount of the discount. Let's use the percent equation to do so. part = percent * whole We are given that the regular price of the drone is $ 640. The store is offering a 10 % discount. If we let d represent the dollar amount of the discount, we can write the following equation. d = 10 % * $ 640 We can write the percent as a decimal before we solve the equation. We will do this by ignoring the percent symbol and moving the decimal point two places to the left.

We found that 10 % is equal to 0.10, or 0.1. d = 10 % * $ 640 [0.3em] ⇓ [0.3em] d = 0.1 * $ 640 Finally, let's compute the right-hand side of the equation. We can ignore the units for now for simplicity.

This means that the dollar amount of the discount is $ 64. Now we can calculate the cost after the discount. $640 - $ 64 = $ 576 The discounted price of the drone is $ 576. The final selling price of the drone will be the discounted price plus the sales tax. We are given that a sales tax of 4.25 % is added after the discount. We can find the dollar amount of the sales tax by using the percent equation again. Let t represent the dollar amount of the sales tax. part = percent * whole ⇓ t = 4.25 % * $ 576 We can write the percent as a decimal by ignoring the percent symbol and moving the decimal point two places to the left.

We found that 4.25 % is equal to 0.0425. t = 4.25 % * $ 576 [0.3em] ⇓ [0.3em] t = 0.0425 * $ 576 Now we will solve the equation for t. Let's ignore the units for now.

We found that the dollar amount of the sales tax is $ 24.48. Finally, let's calculate the final selling price by adding the sales tax to the price after the discount. $576 + $ 24.48 = $ 600.48 The final price of the drone is $ 600.48.