Question

1. Explain whether you would you rather have a savings account that paid interest compounded on a monthly basis or compounded on an annual basis? Why?
2. Describe what an amortization schedule is and its uses. Explain the purpose of an amortization schedule.
3. Interest on a home mortgage is tax deductible. Explain why interest paid in the early years of a home mortgage is more helpful in reducing taxes than interest paid in later years.
4. Explain the difference between an ordinary annuity and an annuity due.

Answer 1

To answer the first question, let us assume that we have two bank savings a/c with deposit of $10000 in each bank namely AB Bank & XY Bank. Now also assume both the banks pay an interest rate of 12% per annum but in case of AB Bank, interest is compounded monthly whereas in case of XY Bank, the intersted is compunded annually.

Now as per formual, we know that, A = P[(1+r/n)^nt] where A= final amount payable by bank, P=Pricipal or amount deposited, r=rate of interest, n= number of times of compounding per year & t=number of year for which the money is invested.  

In case of XY Bank where interest is compounded annually, A=10000[(1+0.12/1)^1*1] or, A=10000(1.12)^1 i.e. $11200.

Whereas in case of AB Bank where interst is compounded monthly, A=10000[(1+0.12/12)^1*12] or, A=10000(1.01)^12 i.e. $11268.25

So we will receive $68.25 more if the interest is compounded monthly when our investment amount and tenure of saving remain constant.

It is better to have a saving account where interest is compounded monthly rather than where interest is compunded annually for the fact that more the number of compounding more will be the interest earned.