Question

Colson and Mark are both investing $1000. Colson invests his $1000 in an account compounding monthly with an APR of r.

Mark splits his investment into two different accounts. Both accounts are compound monthly at an APR of r (which has the same rate as Colson) - but rather with $700 in the first account, and $300 in the second.

Compare the value of these accounts after N years. Clearly explain your reasoning.

Answer 1

ANswer:

Colson 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)

Mark 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 Mark 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.

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