how to solve this questions Consider the balance A(t) of an account with an init

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how to solve this questions

Consider the balance A(t) of an account with an initial investment of $100000 and with a 3.6% APR. Further assume that interest is compounded monthly. This means that the 3.6% annual percentage rate, rather than being paid in total once a year, is paid out in 12 monthly interest payments, each of which pays 3.6/12% or 0.3% interest on the current balance of the account. If you have a choice of two accounts that have the same APR but one is compounded annually and the other is compounded monthly, which should you choose? Why? Complete the following table for the account in Example 2. Note that if interest is compounded monthly, every year the interest is computed and paid 12 times. In each of these computations, the interest rate is one-twelfth of the APR. Therefore, for an account with initial investment A_g, where interest is compounded

Explanation / Answer

10) we will choose compounded monthly

Compounded yearly after n years = (1 +r)^n

=1+nr + nC2 r^2+ ....

= 1 +nr + n(n-1)/(2) r^2 + ...

   Compounded yearly after n years = (1 +r/12)^(12n)

= 1 + 12 n * r/12 + (12n)C2 * (r/12)^2 + ...

= 1 + rn + r^2 * (12 n)(12n -1)/(2*(144)) + ...

= 1 +rn + r^2 (n(n-1/12))/2 + ...

compare the third terms

as n -1/12 > n-1   similarly others

(1 +r/12)^(12n) > (1 +r)^n

b)

months interst balance 0 0 100000 1 300 100300 2 602.7027 100902.7 3 910.8514 101813.6

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