Question

Cole and Anthony are both investing $1000. Cole invests his $1000 in an account compounding monthly with an APR of r. Anthony splits his investment into two accounts. Both accounts compound monthly at an APR of r (the same rate as Cole) but with $700 in the first account, and $300 in the second. . Compare the value of these accounts after N years. Be sure to clearly explain your reasoning.

Answer 1

Cole invests 1000 in an account with an r interest rate compounded monthly for N years.

=> Money after N years = 1000(1+r/12)^(N*12)

Anthony splits investment into 700 and 300 with the same conditions,

=> Money after N years = 700(1+r/12)^(N*12) + 300(1+r/12)^(N*12) = (1+r/12)^(N*12){700+300} = (1+r/12)^(N*12)*1000

The amount will be same for both of them.

The reasons are :

• The tenure of investment is the same
• the interest rate offered in all the accounts are the same and have a compounding effect
• Although Anthony split the investment, the tenure and interest rate are the same so the compounding effect will make the total amount to be equal with the single investment