Answer:
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
