Question

You may wonder why we need to keep more decimal places for interest rates. It is because interest rates are often raised to large powers. Tiny differences in the interest rates may be magnified into great errors after the exponential calculations. To help you make sense of it, let us look at the following example.

• Frank is calculating the monthly mortgage payment for a home buyer (APR-3.8%; principal-$150000; term=30years).

• Given the APR, the monthly interest rate is 0.038/12-0.00317. Frank feel that that number is quite close to 0.003, so he uses 0.003 as the monthly interest rate for his calculations.

• His answer turns out to be 150000/(1/0.003- 1/0.003/1.003^(30*12))=$681.99/month.

• The correct answer should be $698.94. Frank's answer is off by $698.94-$681.991-$16.95/month.

. If he makes this mistake in actual work at a bank, his boss and DDDDDDDDDDD clients will be very unhappy.

• Frank probably does not expect his tiny rounding error (0.00317 instead of 0.003) may cause such a noticeable difference in the final answer!

Question: Suppose for some reason that is unknown to us, Frank mistakenly uses 0.362% as the monthly interest rate. Please find the absolute value of the error in the monthly payment that Frank will get.

Answer 1

If Frank mistakenly uses 0.362% as the monthly interest rate.

So, his answer turns out to be = 150000/(1/0.00362 – (1/0.00362)(1/(1+0.00362)^(30*12))

                                                      = 150000/201.021799 

                                                      = $746.19 

 

The correct answer should be $698.94. 

The absolute value of the error in monthly payment that Frank will get is:

measured value – actual value = $ 746.19 - $698.94

                                                       = $ 47.25/month

The correct answer should be $698.94.