SOLUTION: Teka is saving up money for a down payment on a motorcycle. She currently has $5377, but knows she can get a loan at a lower interest rate if she can put down $6208. If she inves

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Teka is saving up money for a down payment on a motorcycle. She currently has $5377, but knows she can get a loan at a lower interest rate if she can put down $6208. If she inves      Log On


   

Question 1153743: Teka is saving up money for a down payment on a motorcycle. She currently has $5377, but knows she can get a loan at a lower interest rate if she can put down $6208. If she invests the $5377 in an account that earns 4% annually, compounded continuously, how long will it take Teka to accumulate the $6208?
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

6208 = 5377%2Ae%5E%280.04%2At%29,  t is the time in years.


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6208%2F5377 = e%5E%280.04%2At%29


1.154547 = e%5E%280.04%2At%29


Take the natural logarithm of both sides


ln(1.154547) = 0.04*t


t = ln%281.154547%29%2F0.04 = 3.59 of an year, approximately.


So, the answer is:  3.6 years is enough = 3 years and 219 days = 3 years, 7 months and 9 days 
                    (counting 365 days in an year and 30 days in a month).