You deposit

Question

you deposit 1000 at 2% per year in a money market account. what is the balance at the end of one year and what is the annual shield if the interest is 

 

a. simple interest?

b.compounded annually?

c. compounded quarterly?

d. compounded daily?

Answer 1

Do you really mean shield or yield?

 

Anyway, at the end of one year: The balance would 1000 + 1000(.02) = 1020.

 

a. The one that you add to the 1000 at the top is already the simple interest which goes I = Prt = 1000(.02)(1) = 20

 

b. In compound interest, the basic formula is F = P(1+i)ⁿ where P is the present amount and F is the final amount, i is the interest rate and the n is the number of years.

 

F = 1000(1+.02)¹ = 1020, The interest is the difference of Final and Present: 1020 - 1000 = 20.

 

NOTE: You may think that the simple interest and annual compound interest is the same. They're not. It is only true in Year 1, because if you observe the two formulae, the coefficient 1 and exponent 1 in simple and compound interest respectively, don't have any effect in the formula. To further understand this, try t and n be equal to 2.

 

c. For non-annual compound interests, we have a different formula: F = P(1 + i/m)^mn, this formula is actually the shortcut version of it, look up "effective interest rate". The new variable is m, m depends on how you want to compound the interest. Here's a list (semi-annually = 2, quarterly = 4, daily = 365*, monthly = 12). While the n still stays as the number of years.

 

*not sure on that one.

 

F = 1000(1 + .02/4)⁴⁽¹⁾ = 1020.151; I = F - P = 1020.151 - 1000 = 20.151.

 

d. Compounded daily:

 

F = 1000(1+ .02/365)³⁶⁵⁽¹⁾ = 1020.20; I = F - P = 1020.20 - 1000 = 20.20

 

QUICK LESSON: If they have close values then why do they exist? The problem is with the given, 1000 is too small and 1 year is too short. The difference between them will be evident when dealing with larger values and longer periods.