Question - Compound Interest Calculation Function with Variables
Solution:
To write a function for the amount that will be in the account after $$ t $$ years, we can use the formula for compound interest:$$A = P \left(1 + \frac{r}{n}\right)^{nt}$$Where:- $$ A $$ is the amount of money accumulated after $$ n $$ years, including interest.- $$ P $$ is the principal amount (the initial amount of money).- $$ r $$ is the annual interest rate (decimal).- $$ n $$ is the number of times that interest is compounded per year.- $$ t $$ is the time the money is invested for, in years.Given:- $$ P = \$5,280 $$- the annual interest rate $$ r = 4.2\% = 0.042 $$ (as a decimal)- interest is compounded monthly, so $$ n = 12 $$Substitute these values into the compound interest formula to define the function for $$ A $$:$$A(t) = 5280 \left(1 + \frac{0.042}{12}\right)^{12t}$$This function can be used to calculate the amount in the account after any number of years $$ t $$.
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