a student takes out a loan with a 20% monthly compounded interest rate. at the end of the 1st month, the…

a student takes out a loan with a 20% monthly compounded interest rate. at the end of the 1st month, the amount of money owed was $250.\n| # of months | 1 | 2 | 3 | 4 |\n|--|--|--|--|--|--|\n| amount owed | $250 | | | |\nwhat is the explicit equation that could be used to model the total amount owed, f(n), after n months?

a student takes out a loan with a 20% monthly compounded interest rate. at the end of the 1st month, the amount of money owed was $250.\n| # of months | 1 | 2 | 3 | 4 |\n|--|--|--|--|--|--|\n| amount owed | $250 | | | |\nwhat is the explicit equation that could be used to model the total amount owed, f(n), after n months?

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula for a growing quantity is $f(n)=a(1 + r)^{n - 1}$, where $a$ is the initial amount, $r$ is the growth rate, and $n$ is the number of time - periods. Here, the initial amount $a$ is the amount owed at the end of the 1st month, so $a = 250$, and the growth rate $r=0.2$.

Step2: Write the explicit formula

Substitute $a = 250$ and $r = 0.2$ into the formula. We get $f(n)=250(1 + 0.2)^{n - 1}=250\times1.2^{n - 1}$.

Answer:

$f(n)=250\times1.2^{n - 1}$