In 3 years, Caden wants to buy a bicycle that costs 500.00. If he opens a savings account that earns 15% interest compounded continuously, how much will he have to deposit as principal to have enough money in 3 years to buy the bike?

Solution

I n 3 ye a rs, C a d e n w an t s t o b u y a bi cyc l e t ha t cos t s 500.00. I f h e o p e n s a s a v in g s a cco u n t t ha t e a r n s 15% in t eres t co m p o u n d e d co n t in u o u s l y, h o w m u c h w i ll h e ha v e t o d e p os i t a s p r in c i p a l t o ha v e e n o ug h m o n ey in 3 ye a rs t o b u y t h e bik e ?

Principal : 318.81

Solution steps

Translate the problem into an equation:

500 = P e^{0.15 \cdot 3}

Solve for

P, 500 = P e^{0.15 \cdot 3} : P = 318.81

Principal : 318.81