In 1 year, Patrick wants to buy a bicycle that costs 700.00. 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 1 year to buy the bike?

Solution

I n 1 ye a r, P a t r i c k w an t s t o b u y a bi cyc l e t ha t cos t s 700.00. 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 1 ye a r t o b u y t h e bik e ?

Principal : 602.5

Solution steps

Translate the problem into an equation:

700 = P e^{0.15 \cdot 1}

Solve for

P, 700 = P e^{0.15 \cdot 1} : P = 602.5

Principal : 602.5