Question

The same amount of principal is invested in different accounts earning the same interest rate. Which of the following accounts would have the greatest accumulated value at the end of one year?
a.
An account earning no interest
b.
An account earning simple interest
c.
An account earning interest compounded annually
d.
An account earning interest compounded daily

Answer 1

d.

Let the principal be P and the (positive) annual rate be r. After one year:
- no interest: P
- simple interest: P(1 + r)
- compounded annually: P(1 + r)
- compounded daily (n = 365): P(1 + r/365)^{365}.

For n > 1, (1 + r/n)^n > 1 + r, so daily compounding gives the largest accumulated value. (If r = 0 all are equal.)