6. Kody made a deposit into an

account that earns 4% annual

compound interest. After 24

months, the value of his

account was $2,163.20. What

was the amount of Kody's

initial deposit?

Kody made an initial deposit of $2,000

Step-by-step explanation:

Extracting the key information in this question:-

*** Kody's deposit will yield a 4% annual compound interest.

***The initial deposit grew to $2,163.20

*** We are required to calculate the initial deposit he made into the account that later yielded the current amount of $2,163.20.

Before proceeding, we must first put down the formula for calculating compound interest:

Fv = Pv × (1 + r)^t

Where; Fv = the future value

Pv = present value

r = interest rate

t = time

Since we are trying to determine what Kody's initial deposit was before it grew to $2163.20, we will have to make Pv (the present value) the subject of the formula and then solve to find Pv afterwards.

Fv = Pv × (1 + r)^t

Making Pv the subject of the formula:-

Pv = Fv/(1+ r)^t

Here, the future value (Fv) = $2,163.20

the rate (r) = 4% = 0.04

Since the investment is for a period of 24 months, the time is therefore, 2 years.

Substituting accordingly, we have:

Pv = 2,163.20/(1 + 0.04)^2

Pv = 2,163.20/(1.04)^2

Pv = 2,163.20/1.0816

Pv = $2,000

Therefore, Kody made an initial deposit of $2000

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

1 1/5

step-by-step explanation: