How long will it take for 1400 to double if it is invested a

How long will it take for $1,400 to double if it is invested at 12% annual interest compounded 12 times a year? Enter in exact calculations or round to 3 decimal places.

It will take______ years to double.

How long will it take if the interest is compounded continuously?

Compounded continuously, it would only take______ years.

How long does it take for an amount of money P to double itself if its invested at 5% interest compounded 3times a year? Round your answer to 2 decimal places.

It will take ______ years to double.

Solution

Using formula

A = P*(1 + r/n)^nt

P = 1400

r = 12% = 0.12

n = 12 times a year

t = ?

A = 2800

2800/1400 = (1 + 0.12/12)^(12*t)

2 = 1.01^(12*t)

12*t = ln 2/ln (1.01)

t = ln 2/(12*ln 1.01) = 5.805 years

part B.

A = P*e^(r*t)

A = 2800

P = 1400

r = 12% = 0.12

2800/1400 = 2 = e^(12*t)

t = (ln 2)/0.12 = 5.776 years

Part C

A = 2*P

2 = (1 + 0.05/3)^(3*t)

3*t = ln 2/(ln (1 + 0.05/3))

t = ln 2/(3*ln (1 + 0.05/3)) = 13.97 years