Gabriel and Belle deposited 10,000.00 into a savings account which earns interest compounded continuously. After 1 year, they had 11,039.00 in the account which they used to go on a trip. What was the interest rate on the account?

Solution

G ab r i e l an d B e ll e d e p os i t e d 10, 000.00 in t o a s a v in g s a cco u n t w hi c h e a r n s in t eres t co m p o u n d e d co n t in u o u s l y . A f t er 1 ye a r, t h ey ha d 11, 039.00 in t h e a cco u n t w hi c h t h ey u se d t o g o o n a t r i p . Wha t w a s t h e in t eres t r a t e o n t h e a cco u n t ?

Rate : 9.88493 \dots %

Solution steps

Translate the problem into an equation:

11039 = 10000 e^{r \cdot 1}

Solve for

r, 11039 = 10000 e^{r \cdot 1} : r = 9.88493 \dots %

Rate : 9.88493 \dots %