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. Because the interest is compounded more frequently, you will get more money. This is because it allows you to earn interest on previous interest more frequently. 

Answer 2

Answer : D

The same amount of principal is invested in different accounts earning the same interest rate.

The account will not grow without interest

Lets assume , initial amount P= 100, rate of interest = 5%=>r= 0.05 and

number of years, t= 1

Calculate the simple interest

A = P + P*r*t = 100 + 100*.05*1= 105

In simple interest, $100 invested , amount earned = $105

Now we calculate earning interest compounded annually

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

Lets assume , initial amount P= 100, rate of interest = 5%=>r= 0.05 and

number of years, t= 1, for compounded annually n= 1

`A= 100(1+(0.05)/(1))^(1*1)`= 105

For interest compounded annually, $100 invested , amount earned = $105

Now we calculate earning interest compounded daily

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

Lets assume , initial amount P= 100, rate of interest = 5%=>r= 0.05 and

number of years, t= 1, for compounded annually n= 365

`A= 100(1+(0.05)/(365))^(1*365)`= 105.26

For interest compounded daily, $100 invested , amount earned = $105.26

So, An account compounded daily will have greatest accumulated value at the end of one year