An initial amount of 3100 is invested in an account at an interest rate of 3% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after six years.Do not round any intermediate computations, and round your answer to the nearest cent.

Solution

implicit derivative

ini t ia l am o u n t o f 3100 i s in v es t e d in an a cco u n t a t an in t eres t r a t e o f 3% p er ye a r, co m p o u n d e d co n t in u o u s l y . A ss u min g t ha t n o w i t h d r a w a l s a re ma d e, f in d t h e am o u n t in t h e a cco u n t a f t er s i x ye a rs . Do n o t ro u n d an y in t er m e d ia t e co m p u t a t i o n s, an d ro u n d yo u r an s w er t o t h e n e a res t ce n t .

Amount : 3711.37

Solution steps

Translate the problem into an equation:

A = 3100 e^{0.03 \cdot 6}

3100 e^{0.03 \cdot 6} = 3711.37382 \dots

Round to the nearest hundredth:

3711.37

Amount : 3711.37