Question

7. For the compound interest loan whose terms are given below, find the principal required to reach the given future value at the end of the specified time. Future value: $3500 Interest rate: 3.8% Compounding: Continuously Time: 1.5 years Principal: $

Answer 1

In order to calculate the principal, we can use the formula for interest compounded continuously:

$A=P\cdot e^{rt}$

Where A is the final amount after t years, P is the principal, r is the interest rate and e is a constant equal to 2.7183.

So we have:

$\begin{gathered} 3500=P\cdot2.7183^{0.038\cdot1.5} \\ 3500=P\cdot1.058656 \\ P=\frac{3500}{1.058656}=3306.08 \end{gathered}$

So the principal is $3306.08.