Question

Find the amount A=? if $20,000 is invested with the APR rate of 6% compounded continuously for 5 years. Round the answer in two places.

Answer 1

$26,997.18

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Interest 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:

• P = $20,000
• r = 6% = 0.06
• t = 5 years

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

`\implies A=20000e^((0.06 \cdot 5))`

`\implies A=20000e^(0.3)`

`\implies A=20000 \cdot 1.3498588...`

`\implies A=26997.17615152...`

`\implies A=26997.18\;(\sf 2\;d.p.)`

Therefore, the amount in the account is $26,997.18 (nearest cent).