7. a person loans his friend $500. they agree to an annual interest rate of 5%. write an expression for…
7. a person loans his friend $500. they agree to an annual interest rate of 5%. write an expression for computing the amount owed on the loan, in dollars, after t years if no payments are made.
Answer
Explanation:
Step1: Recall compound - interest formula
The compound - interest formula for the amount $A$ when the principal $P$ is compounded annually at an interest rate $r$ for $t$ years is $A = P(1 + r)^t$. Here, since it's simple interest - like situation (no mention of compounding frequency other than annual and no payments), we can also use the simple - interest formula $A=P(1 + rt)$ where $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the number of years. The principal $P = 500$, and the annual interest rate $r=0.05$ (since $5%=0.05$).
Step2: Substitute values into formula
Substitute $P = 500$ and $r = 0.05$ into the formula $A=P(1 + rt)$. We get $A = 500(1+0.05t)$.
Answer:
$500(1 + 0.05t)$