Question

a. You deposit $4000 in an account which pays 4% compounded continuously. How much will you have at the end of 20 years? Round to the nearest penny. 

b. Find the doubling time for 3% compounded continuously. Do not use the Rule of 72. 

Answer 1

a) solutions:

Compound Interest formula

A = P (1 + r)ⁿ

, A=Amount at end ,P = invested amount ,n=time ,r=interest rate

​​​​​​Having amount at end of 20 year=$4000(1+0.04)²⁰

=$4000 X 2.191123143 =$ 8764.50

b) solutions:

Amount at end (A) = 2 X invested Amount (2P)

On putting value in compound interest formula

(A)2P = P(1+0.03)ⁿ

Or 2 X $4000 = $4000 X 1.03ⁿ

Or 2 =1.03ⁿ

Taking Ln in both side

ln 2 = n ln 1.03

Or n =ln 2 / ln 1.03

Or n = 23.45 years

Doubling time is 23.45 years.