Question

doug paid a maturity value of $5071.50 on a 2-year note with annual interest of 5% (or 0.05). use the formula $m = p(1 + r)^n$, where $n$ is the number of years in the problem, to find the amount borrowed.

doug borrowed $\square$
(simplify your answer.)

Explanation:

Step1: Identify known values

We know that \( M = 5071.50 \), \( r = 0.05 \), and \( n = 2 \). The formula is \( M = P(1 + r)^n \). We need to solve for \( P \).

Step2: Rearrange the formula to solve for \( P \)

From \( M = P(1 + r)^n \), we can rearrange it to \( P=\frac{M}{(1 + r)^n} \).

Step3: Substitute the known values into the formula

Substitute \( M = 5071.50 \), \( r = 0.05 \), and \( n = 2 \) into the formula:
First, calculate \( (1 + r)^n=(1 + 0.05)^2=(1.05)^2 = 1.1025 \)
Then, \( P=\frac{5071.50}{1.1025} \)

Step4: Perform the division

\( \frac{5071.50}{1.1025}=4600 \)

Answer:

4600