Katie deposited 2,000 into a new savings account that paid interest at an annual rate of 3%, compounded continuously. If there were no other transactions, approximately how much money was in Katie’s account 6 years after she made the deposit?

Solution

K a t i e d e p os i t e d 2, 000 in t o a n e w s a v in g s a cco u n t t ha t p ai d in t eres t a t an ann u a l r a t e o f 3%, co m p o u n d e d co n t in u o u s l y . I f t h ere w ere n o o t h er t r an s a c t i o n s, a pp ro x ima t e l y h o w m u c h m o n ey w a s in K a t i e ’ s a cco u n t 6 ye a rs a f t er s h e ma d e t h e d e p os i t ?

Amount : 2394.43

Solution steps

Translate the problem into an equation:

A = 2000 e^{0.03 \cdot 6}

2000 e^{0.03 \cdot 6} = 2394.43472 \dots

Round to the nearest hundredth:

2394.43

Amount : 2394.43