Question

You deposited $800 into an account paying 4.5% interest compounded continuously. A. How much would be in the account in 5 years? B. How long would it take to double your money?

Answer 1

Explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

A) From the information given,

P = $800

r = 4.5% = 4.5/100 = 0.045

t = 5 years

Therefore,

A = 800 x e^(0.045 x 5)

A = 800 x e^(0.225)

A = $1002

B) For it to double,

A = 2 × 800 = 1600

Therefore,

1600 = 800 x e^(0.045 x t)

1600/800 = e^(0.045t)

2 = e^(0.045t)

Taking ln of both sides, it becomes

Ln2 = 0.045t

0.693 = 0.045t

t = 0.693/0.045

t = 15.4 years