Question

How long does it take for a deposit of $1400 to double at 2% compounded continuously?

Answer 1

34.66 yr

Explanation:

The formula for interest compounded continuously is

`A = Pe^(rt)`

Data:

P = $1400

r = 2 % = 0.02

Calculations:

(a) Calculate A

A = 2 × 1400 = $2800

(b) Calculate t

`2800 = 1400e^(0.02t)`

`2 = e^(0.02t)` Divided each side by 1400

ln2 = 0.02t Took the ln of each side

t = ln2/0.02 Divided each side by 0.02

t = 34.66 yr

It will take 34.66 yr for the investment to double at 2 % interest compounded continuously.

Check:

2800 = 1400e^{0.02×34.66}

2800 = 1400e^{0.6931}

2800 = 1400 × 2

2800 = 2800