In 1 year, Steven wants to buy a bicycle that costs 2,000.00. If he opens a savings account that earns 10% 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, St e v e n w an t s t o b u y a bi cyc l e t ha t cos t s 2, 000.00. 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 10% 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 : 1809.67

Solution steps

Translate the problem into an equation:

2000 = P e^{0.1 \cdot 1}

Solve for

P, 2000 = P e^{0.1 \cdot 1} : P = 1809.67

Principal : 1809.67