Suppose that 2700 is borrowed for seven years at an interest rate of 5% per year, compounded continuously. Find the amount owed, assuming no payments are made until the end. Do not round any intermediate computations, and round your answer to the nearest cent.

Solution

S u pp ose t ha t 2700 i s b orro w e d f or se v e n ye a rs 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 . F in d t h e am o u n t o w e d, a ss u min g n o p a y m e n t s a re ma d e u n t i l t h e e n d . 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 : 3831.48

Solution steps

Translate the problem into an equation:

A = 2700 e^{0.05 \cdot 7}

2700 e^{0.05 \cdot 7} = 3831.48238 \dots

Round to the nearest hundredth:

3831.48

Amount : 3831.48