Emmett opened a savings account and deposited 400.00. The account earns 13% interest, compounded continuously. If he wants to use the money to buy a new bicycle in 1 year, how much will he be able to spend on the bike?

Solution

E mm e tt o p e n e d a s a v in g s a cco u n t an d d e p os i t e d 400.00. T h e a cco u n t e a r n s 13% in t eres t, co m p o u n d e d co n t in u o u s l y . I f h e w an t s t o u se t h e m o n ey t o b u y a n e w bi cyc l e in 1 ye a r, h o w m u c h w i ll h e b e ab l e t o s p e n d o n t h e bik e ?

Amount : 455.53

Solution steps

Translate the problem into an equation:

A = 400 e^{0.13 \cdot 1}

400 e^{0.13 \cdot 1} = 455.53135 \dots

Round to the nearest hundredth:

455.53

Amount : 455.53