Suppose Mary deposits $200 at the end of each month for 30 years into an account that pays 5% interest compounded monthly.

Question

Question 1: How much total money will she have in the account at the end?

Question 2: How much total money did Mary actually deposit?

Question 3: How much total interest did the account earn over that period?

Question 4: Suppose instead of making monthly deposits, Mary decides to deposit a “lump sum” into the account. How much must she deposit? What is this value also called?

Answer 1

QUESTION 1: The relevant formula is:

 

                     (1 + r/n)^nt - 1

FV = MD * --------------------

                             r/n

 

Where:

 

FV = Future Value

MD = Monthly deposit = $200

n = compounding periods per year = 12

t = years = 30

r = annual interest rate = 5% = 0.05

 

                          (1 + 0.05/12)^12*30 - 1
FV = ($200) *  ------------------------------
                                   0.05/12

 

                           (1.00417)³⁶⁰ - 1
FV = ($200) *  -----------------------                            

                               0.00417

 

FV = $166,318.67

 

QUESTION 2:  Mary deposited ($200/month)*(12 months/year)*(30 years) = $72,000

 

QUESTION 3: Interest Earned =  ($166,318.67) - ($72,000) =  $94,318.67

 

QUESTION 4:  For a single lump sum deposit, the formula is:

 

FV = P*(1 + r/n)^nt

 

Solving for P, the lump sum deposit:

 

P = FV/(1 + r/n)^nt = ($166,318.67)/(1.00417)³⁶⁰ = $37,235.44

 

P is short for "Principle", aka "Present Value"