Devin and Clare deposited 3,962.00 into a savings account which earns interest compounded continuously. After 1 year, they had 4,487.00 in the account which they used to go on a trip. What was the interest rate on the account?

Solution

De v in an d Cl a re d e p os i t e d 3, 962.00 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 4, 487.00 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 : 12.44353 \dots %

Solution steps

Translate the problem into an equation:

4487 = 3962 e^{r \cdot 1}

Solve for

r, 4487 = 3962 e^{r \cdot 1} : r = 12.44353 \dots %

Rate : 12.44353 \dots %