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

$120,821.88 (nearest cent)

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=(200000)/(e^(0.504))`

`\implies \sf P=120821.8766...`

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

Answer 2

• $120821.83

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`