Question

NO LINKS!! How much money, invested at an interest rate of r% per year compounded continuously, will amount to A dollars after t years? (Round your answer to the nearest cent.) Part 2v​

Answer 1

Answer:

• $120821.83

Step-by-step explanation:

Use continuous compound equation:

• $A = P*e^{rt}$, where A- future amount, P- invested amount, t- time, r- rate

Given

• A = $200000,
• r = 3.6% = 0.036,
• t = 14 years.

Plug in and solve for P

• $200000 = P*e^{0.036*14}$
• $200000=P*1.65533$
• $P=200000/1.65533$
• $P=120821.83$

Answer 2

Answer:

$120,821.88 (nearest cent)

Step-by-step explanation:

Continuous Compounding Formula

$\large \text{ \sf A=Pe^{rt} }$

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:

$\implies \sf 200000=P \cdot e^{0.036 \cdot 14}$

$\implies \sf 200000=P \cdot e^{0.504}$

$\implies \sf P=\dfrac{200000}{e^{0.504}}$

$\implies \sf P=120821.8766...$

Therefore, the principal amount invested was $120,821.88 (nearest cent).