Question

Find the final amount of an investment of $900 earning a quarterly interest rate or 6% compounded continuously for 15 years. Find Pę^rt

Answer 1

`A=Pe^(rt)`

A is the final amount

P is the principal

r is the interest rate in decimal form

t is the time in years

For the given situation:

`\begin{gathered} P=900 \\ \\ r=(1+(i)/(n))^n-1 \\ i=0.06 \\ n=4\text{ \lparen}quarterly) \\ r=(1+(0.06)/(4))^4-1 \\ r=1.015^4-1 \\ r=1.061-1 \\ r=0.06 \\ \\ t=15 \\ \\ A=900*e^(0.06*15) \\ A\approx2213.64 \end{gathered}`

Then, the final amount is $2213.64