Answer:
$120,821.88 (nearest cent)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
- A = Final amount.
- P = Principal amount.
- e = Euler's number (constant).
- r = Annual interest rate (in decimal form).
- t = Time (in years).
Given values:
- A = $200,000
- r = 3.6% = 0.036
- t = 14 years
Substitute the given values into the formula and solve for P:
[tex]\implies \sf 200000=P \cdot e^{0.036 \cdot 14}[/tex]
[tex]\implies \sf 200000=P \cdot e^{0.504}[/tex]
[tex]\implies \sf P=\dfrac{200000}{e^{0.504}}[/tex]
[tex]\implies \sf P=120821.8766...[/tex]
Therefore, the principal amount invested was $120,821.88 (nearest cent).
