An initial amount of 2100 is invested in an account at an interest rate of 5% per year, compounded continuously. Assuming that no withdrawals are made, find the amount in the account after two years. Do not round any intermediate computations, and round your answer to the nearest cent.

해법

A n ini t ia l am o u n t o f 2100 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 5% 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 tw o 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 : 2320.86

솔루션 단계

Translate the problem into an equation:

A = 2100 e^{0.05 \cdot 2}

2100 e^{0.05 \cdot 2} = 2320.85892 \dots

가장 가까운 hundredth 으로 반올림:

2320.86

Amount : 2320.86