Problema Solution
Donnie is saving up money for a down payment on a car. He currently has
$5194, but knows he can get a loan at a lower interest rate if he can put down
$6096. If he invests the
$5194 in an account that earns
5.5% annually, compounded continuously, how long will it take Donnie to accumulate the
$6096? Round your answer to two decimal places, if necessary.
Answer provided by our tutors
Let
P = $5,194 the principal (the investment)
t = the time in years
r = 0.055 or 5.5% the annual interest rate
A = $6096 the future value (the investment will double in size)
The future value formula for continuous compounding is:
A=Pe^(rt)
Plug the values into the formula:
6096= 5194e^(0.055t)
e^(0.055t) = 6096/5194
e^(0.055t) = 1.17366
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t = 2.91 years
It will take 2.91 years for the investment to accumulate the $6096.