In 1 year, Krysta wants to buy a bicycle that costs 3,000.00. If she opens a savings account that earns 5% interest compounded continuously, how much will she have to deposit as principal to have enough money in 1 year to buy the bike?

Solution

I n 1 ye a r, Krys t a w an t s t o b u y a bi cyc l e t ha t cos t s 3, 000.00. I f s 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 5% 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 s 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 : 2853.69

Solution steps

Translate the problem into an equation:

3000 = P e^{0.05 \cdot 1}

Solve for

P, 3000 = P e^{0.05 \cdot 1} : P = 2853.69

Principal : 2853.69