Find the time required for the amount to (a) double and (b) triple.

Question

$2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to (a) double and (b) triple.

r = 0.05

Answer 1

Step 1 :

(a)

Total amount .

The rate of interest is

Since the amount is doubled,

Formula for continuous compounding is

Substitute and in above equation.

Apply logarithm on each side.

Use the formula :

The time required for the amount to be double is 13.863 years.

Step 2 :

(b)

Since the amount is tripled,

Formula for continuous compounding is

Substitute and in above equation.

Apply logarithm on each side.

Use the formula :

The time required for the amount to be triple is 21.972 years.

Solution :

(a) The time required for the amount to be double is 13.863 years.

(b) The time required for the amount to be triple is 21.972 years.