Question

Ariana has a choice of two investments. She can invest $12,000 at 5% for 8 years, or she can invest $9000 at 6.5% for 7 years. Both accounts are compounded continuously. Which investment will result in the greater amount of interest earned.

Answer 1

Answer:

 $12000 at 5% for 8 years

Step-by-step explanation:

The amount in an account earning continuous interest is given by ...

  A = Pe^(rt)

Then the interest earned is ...

  I = P(e^(rt) -1)

For the two accounts, the interest earned is ...

  I = 12000(e^(.05·8) -1) = 12000(0.491825) = 5901.90

  I = 9000(e^(0.065·7) -1) = 9000(0.576173) = 5185.56

The $12000 account earns more interest, primarily because of the larger amount invested.