Greg wanted to buy a new guitar. Greg deposited 100.00 into a new savings account that earns interest compounded continuously. After 1 year, he withdrew the entire balance of 114.00 and bought the guitar. What was the interest rate on the account?

Solution

G re g w an t e d t o b u y a n e w gu i t a r . G re g d e p os i t e d 100.00 in t o a n e w s a v in g s a cco u n t t ha t 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, h e w i t h d re w t h e e n t i re ba l an ce o f 114.00 an d b o ug h t t h e gu i t a r . 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 : 13.10282 \dots %

Solution steps

Translate the problem into an equation:

114 = 100 e^{r \cdot 1}

Solve for

r, 114 = 100 e^{r \cdot 1} : r = 13.10282 \dots %

Rate : 13.10282 \dots %