Carmen needs $3560 for future project. She can invest $2000 now at annual rate of 7.8%, compound monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

Question

Mathematics

Joel Wilson

7 September, 02:12

Carmen needs $3560 for future project. She can invest $2000 now at annual rate of 7.8%, compound monthly. Assuming that no withdrawals are made, how long will it take for her to have enough money for her project?

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Answers (2)

Know the Answer?

Anton Morrison · Answer 1

Anton Morrison 7 September, 03:18

0

I'm not sure I think it's 10

Madden Oconnell · Answer 2

7.42 years (7 years 5 months)

Step-by-step explanation:

The future value of Carmen's account can be modeled by

FV = P (1 + r/12) ^ (12t)

where P is the principal invested, r is the annual rate, and t is the number of years.

Solving for t, we have ...

FV/P = (1 + r/12) ^ (12t)

log (FV/P) = 12t·log (1 + r/12)

t = log (FV/P) / (12·log (1 + r/12))

For FV = 3560, P=2000, r = 0.078, the time required is ...

t = log (3560/2000) / (12·log (1 +.078/12))

t ≈ 7.42

It will take Carmen about 7 years 5 months to reach her savings goal.