Question

Question

Tim has an investment account that compounds interest continuously at a rate of 1.6%. After 5 years, he has $2400 in the
account.
How much money did he initially place in the account?
Round your answer to the nearest dollar.

Answer 1

$2215

Explanation:

The formula for continuous compound interest is P(t) = P₀
`e^(rt)`.

$2,400 = P₀e⁽¹⁻⁰¹⁶⁾⁽⁵⁾

Divide both sides by (e⁽¹⁻⁰¹⁶⁾⁽⁵⁾) to isolate the initial amount:

($2,400) ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = (P₀e⁽¹⁻⁰¹⁶⁾⁽⁵⁾) ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾

$2,400 ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = P₀

Solve:

$2,400 ÷ e⁽¹⁻⁰¹⁶⁾⁽⁵⁾ = $2215.48

P₀ = $2215.48

P₀ = $2215

Hope this helps!