ricardo torres invests 10000 at 4 percent compounded daily f

ricardo torres invests 10000 at 4 percent compounded daily for 1 year, at the end of the year, torres reinvested he amount in the account for another year at the same rate. He repeats this process for 2 more years. compare the amount in the account at the end of 4 years with what he would have had if he had invested the $10000 at 4% compounded daily for 4 years?

the answer in the book says 11734.99 vs 11735.01 which is a $.02 difference. But I want know the process. The interest rate of 10000 at 4 percent compounded daily for 1 year is 1.010808

Solution

Given,

P = 10000, r = 4%/365(compounded daily), t = 1yr*365

Now, principle becomes, after 1 yr with daily compounding

10000(1+.04/365)³⁶⁵

10000(1.040808),

Since this amount is reinvested for 3 more years,

Principle becomes,

10000(1.040808)⁴

This comes to 11734.99

On the other hand, if it is directly calculated with 4 years compounding daily, principle becomes

10000(1+.04/365)¹⁴⁶⁰

This comes to 10000(1.17350058)

11735.01(Rounded)