Question

Wei deposits 3000 at time 0, and 2000 at time 2 in an account that earns interest at an effective rate i. His account balance at time 5 is twice as large as at time 1. Determine i.

Answer 1

Account balance at time 5: 2000(1+i)^5

Account balance at time 1: 2000(1+i)^1

As per question;

2000(1+i)^5={2000(1+i)^1}×2

or, (1+i)^5/(1+i)^1=4000/2000

or, (1+i)^4=2

or, (1+i)=2^1/4

or, (1+i)=1.189

or, i=1.189-1

or, i=0.189=19%(Approx)

Summary:

Firstly we have computed the account balance after 5 year by using compund interest formula and then we calculate account balance after 1 year. And as per question after 5 year account balance will be twice than 1st year.Then we apply it and calculate the interest rate.