find the future value of the loan. round your answer to the nearest cent.\n$p = \\$4550, r = 6.46\\%, t = 7$…

find the future value of the loan. round your answer to the nearest cent.\n$p = \\$4550, r = 6.46\\%, t = 7$ years\nthe future value of the loan is $\\square$.

find the future value of the loan. round your answer to the nearest cent.\n$p = \\$4550, r = 6.46\\%, t = 7$ years\nthe future value of the loan is $\\square$.

Answer

Explanation:

Step1: Convert the interest rate to decimal

The interest rate $r = 6.46%=0.0646$.

Step2: Use the simple - interest future - value formula

The formula for the future value $A$ of a loan with principal $P$, annual interest rate $r$, and time $t$ (in years) is $A = P(1 + rt)$. Here, $P = 4550$, $r=0.0646$, and $t = 7$. Substitute the values into the formula: $A=4550\times(1 + 0.0646\times7)$.

Step3: Calculate the value inside the parentheses first

$0.0646\times7=0.4522$. Then $1 + 0.4522 = 1.4522$.

Step4: Calculate the future value

$A = 4550\times1.4522=4550\times1.4522 = 6607.51$.

Answer:

$6607.51$