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Monique wants to invest 4000 in a savings account that pays 3.4% annual interest compounded continuously. How long will it take her to have 4500 in her account? Round your answer to the nearest tenth of a year.

Solution

M o ni q u e w an t s t o in v es t 4000 in a s a v in g s a cco u n t t ha t p a ys 3.4% ann u a l in t eres t co m p o u n d e d co n t in u o u s l y . Ho w l o n g w i ll i t t ak e h er t o ha v e 4500 in h er a cco u n t ? R o u n d yo u r an s w er t o t h e n e a res t t e n t h o f a ye a r .

Time : 3.5

Solution steps

Translate the problem into an equation:

4500 = 4000 e^{0.034 t}

Solve for

t, 4500 = 4000 e^{0.034 t} : t = 3.46420 \dots

Time : 3.46420 \dots

Round

3.46420 \dots

to the nearest tenth:

3.5

Time : 3.5