Question

Suppose that Upper P 0 is invested in a savings account in which interest is compounded continuously at 6.4​% per year. That​ is, the balance P grows at the rate given by the following equation. StartFraction dP Over dt EndFraction equals 0.064​P(t) ​(a) Find the function​ P(t) that satisfies the equation. Write it in terms of Upper P 0 and 0.064. ​(b) Suppose that ​$500 is invested. What is the balance after 3 ​years? ​(c) When will an investment of ​$500 double​ itself?

Answer 1

(B) $602.2750

(C) 11.72 years

Step-by-step explanation:

(A)

The compound interest formula is

`Principal * (1+ r)^(time) = Ammount`

(B)

`Principal * (1+ r)^(time) = Ammount`

`500 * (1.064)^(3) = 602.2750`

(C)

`1(1.064)^(time) = 2\\\\log_(1.064)\: 2= time\\\\(log 2)/(log 1.064) = 11.717341521`