Question

1. Find the interest earned on $50,000 deposited for 6 years at 4 1/8 % interest, compounded continuously

Answer 1

First, we will remember the formula for compound interest.

The compound interest formula

`A=P(1+r)^t`

Where P stands for the principal (or the value deposited), t the time and r the annual interest rate in decimal, and A the value obtained after the time.

For finding the interest earned, we should make the difference between the future value and the initial deposit.

Finding the future value.

We will just apply the above formula, having in mind that in this exercise,

`\begin{gathered} P=50000 \\ t=6 \\ r=4(1)/(8)\text{ \%} \end{gathered}`

Which means that

`r=0.04125=4,125\text{ \%}`

And we have all the values. Now,

`\begin{gathered} A=P(1+r)^t \\ A=50000(1+0.04125)^6 \end{gathered}`

And we do the opperations inside the parenthesis:

`\begin{gathered} A=50000(1.04125)^6 \\ A=50000(1.27447) \\ A=63723.56889 \end{gathered}`

This would mean, the future value will be $63 723.568.

Finding the interest

The last step will be making the substraction, so

`I=A-P=63723.57-50000=13723.57`

And then, the interest earned will be of $13 723.57.