A starting principal of 6000 continuously compounds for 8 years, resulting in an acquired amount of 9000. Find the interest rate that produced this amount. Answer as a percentage rounded to two decimal places.

Solution

A s t a r t in g p r in c i p a l o f 6000 co n t in u o u s l y co m p o u n d s f or 8 ye a rs, res u lt in g in an a c q u i re d am o u n t o f 9000. F in d t h e in t eres t r a t e t ha t p ro d u ce d t hi s am o u n t . A n s w er a s a p erce n t a g e ro u n d e d t o tw o d ec ima l pl a ces .

Rate : 5.19895 \dots %

Solution steps

Translate the problem into an equation:

9000 = 6000 (1 + \frac{r}{1})^{1 \cdot 8}

Solve for

r, 9000 = 6000 (1 + \frac{r}{1})^{1 \cdot 8} : r = 5.19895 \dots %

Rate : 5.19895 \dots %