Question

Nicole invests a sum of money in a retirement account with a fixed annual interest rate of 6 percent compounded continuously. After 17 years, the balance reaches $8,441.60. What was the amount of the initial investment?

Round your answer to the nearest TENs place.

Answer 1

$3,040.00

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^(rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}`

Given:

• A =$8,441.60
• r = 6% = 0.06
• t = 17 years

Substitute the given values into the continuous compounding formula and solve for P:

`\implies 8441.60=Pe^(0.06 * 17)`

`\implies 8441.60=Pe^(1.02)`

`\implies P=(8441.60)/(e^(1.02))`

`\implies P=3043.99824...`

Therefore, the amount of the initial investment is $3,040.00 (rounded to the nearest tens place).