Suppose that \$2200 is borrowed for five years at an interest rate of 4.5% 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 $2200 i s b orro w e d f or f i v e ye a rs a t an in t eres t r a t e o f 4.5% 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 : 2755.11

Solution steps

Translate the problem into an equation:

A = 2200 e^{0.045 \cdot 5}

2200 e^{0.045 \cdot 5} = 2755.10997 \dots

Round to the nearest hundredth:

2755.11

Amount : 2755.11