Question

Finding the initial amount in a word problem on continuous compound interest

Answer 1

Answer:

Explanation:

We'll use the below compound interest formula to solve the given problem;

$A=Pe^{rt}$

where A = Final amount = $5000

P = Initial amount = ?

r = interest rate in decimal = 4% = 4/100 = 0.04

t = time = 7 years

Let's go ahead and substitute the above values into our formula and solve for P as seen below;

$\begin{gathered} 5000=Pe^{0.04(7)} \\ 5000=Pe^{0.28} \\ 5000=1.32312981234P \\ P=\frac{5000}{1.32312981234} \\ P=3778.92 \end{gathered}$

We can see from the above that Miguel should pay for $3778.92