algebra word problem

Question

When interest is compounded continuously, the balance in an account after t years is given by

A = Pert,

Where P is the initial investment (i.e., the principal) and r is the interest rate (expressed as a decimal).

a) Maya has deposited $500 in an account that pays 6.75% interest, compounded

continuously. How long will it take for her money to double?
b) Suppose that $1000 is invested at a rate of 5% per year compounded continuously. What is the balance after 2 yrs?

Answer 1

b. A(t) = Pe^rt, where A(t) is the amount in the account in t years

 

    A(2) = 1000e^0.05(2)  = 1000e^0.1 = $1105.17

Answer 2

a.

1000 = 500e^0.0675t

2 = e^0.0675t                               take natural log of both sides

ln 2 = 0.0675t

0.0693147181 ≈ 0.0675t

10.2688471 ≈ t

 

b. 

A = 1000 + 1000e^0.05(2)

A = 1000 + 1000e^0.1

A ≈ 1000 + 1000(1.10517092)

A ≈ 1000 + 1105.17092

A ≈ 2105.17092