tom borrowed $8000 at a rate of 12.5%, compounded annually. assuming he makes no payments, how much will he…

tom borrowed $8000 at a rate of 12.5%, compounded annually. assuming he makes no payments, how much will he owe after 8 years? do not round any intermediate computations, and round your answer to the nearest cent.

tom borrowed $8000 at a rate of 12.5%, compounded annually. assuming he makes no payments, how much will he owe after 8 years? do not round any intermediate computations, and round your answer to the nearest cent.

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, 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 (in decimal form), and $t$ is the time the money is invested or borrowed for in years.

Step2: Convert the interest rate to decimal

The annual interest rate $r = 12.5%=0.125$, the principal amount $P=$8000$, and the time $t = 8$ years.

Step3: Substitute values into the formula

Substitute $P = 8000$, $r=0.125$, and $t = 8$ into the formula $A = P(1 + r)^t$. We get $A=8000\times(1 + 0.125)^8$.

Step4: Calculate $(1 + 0.125)^8$

$(1 + 0.125)^8=(1.125)^8\approx2.56329$.

Step5: Calculate the final amount

$A = 8000\times2.56329=$20506.32$.

Answer:

$20506.32$