Question

When you make a large purchase (say, a house or a car) you typically borrow money from lenders (e.g. banks, mortgage brokers, credit unions, etc.) who frequently quote the interest you are going to pay in two ways. First, they quote an annual 'interest rate' - the number they widely advertise (but which is often inaccurate), and then a higher (sometimes, much higher) "APR"- which they don't advertise but HAVE to disclose in the fine print because of regulation. The latter number (the "APR") includes all upfront costs generated by the "loan origination" process and reflects your true annualized costs (hence its name "Annual Percentage Rate").

In this discussion, please go online and find two lenders with the largest difference between their APRs (BankRate.com will be useful here) in your area. Make the following assumptions:

1. The value of the house, the down payment, and how much you will borrow.

2. Assume you are taking 30-year fixed mortgage - they are the simplest to deal with.

Calculate the monthly mortgage payments using APRs for both the highest and lowest interest rate lender (or use BankRate's numbers). Calculate the difference in these monthly payments.

Most important: assume that you can invest the DIFFERENCE in monthly payments in the stock market at 0.5% monthly rate of return. How much money would you accumulate by the end of the mortgage (in 360 months) had you invested with the lowest APR lender instead of the highest? What is this value closest to in consumer products? (e.g. iPhone, one-week Hawaii vacation, etc. - be creative).

Answer 1

Solution: The question is answered based on the workings shown below:-

			Explanations
Bank of America	7.83%	APR	Data taken from Bankrate.com
Third Federal	4.49%	APR	Data taken from Bankrate.com
Value of the House	1000000	Dollars	Assumption
Down Payment (10%)	100000	Dollars	Assumption
Borrowing (90%)	900000	Dollars	Assumption
Time	30	years	Provided in the Question
Nper in Months	360		Provided in the Question
Monthly Rate BoA	0.65%		=7.83%/12
Monthly Rate Third Federal	0.37%		=4.49%/12
Monthly Payment BoA	$6,497.54		Use formula Present Value Annuity 900000 = Annuity*[1-(1/1+0.65%)^-360 / 0.65%]
Monthly Payment Third Federal	$4,554.82		Use formula Present Value Annuity 900000 = Annuity*[1-(1/1+0.37%)^-360 / 0.37%]
Difference between Monthly mortgage payment after borrowing from Lower APR lender	$1,942.71		=$6497.54-$4554.82
Investing difference amount	$1,942.71		Asked in the question
Monthly Rate	0.50%		Provided in the Question
Nper in Months	360		Provided in the Question
Value after 360 months by investing the difference amount at 0.50%	$11,700.14		Use formula related to Future Value= 1942.71 * (1+0.50%)^360
We should spend on a Tiffany & Co.'s "Tiffany Setting" one-carat engagement ring @ $11,000