Question

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

Answer 1

Step-by-step 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=(5000)/(1.32312981234) \\ P=3778.92 \end{gathered}`

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