The lowest 30-rate mortgage rate

Search the internet and find the lowest 30-rate mortgage rate for the period from 1971 to now
(e.g., check http://www.freddiemac.com/pmms/pmms30.htm). The point-measure refer to the
mortgage fee as a percentage of the loan. For instance, a mortgage of $1m and a point-variable of
0.7 implies that, in addition to the interest, a fee of $7,000 is due up front.
a) When (what year and month) did the rate reach its historical low; how high was the rate?
Assuming a growth rate g=0 and disregarding the fee point-variable, what would the
resulting price-to-rent ratio be?
now, Oct 2020, 2.83% 1/0.0283=35.34
b) When (what year and month) did the rate reach its historical high; how high was the rate?
Assuming that R*=R, what is the ratio NPV/R?
Oct 1981: 18.45%, NPV/P=1/.1845=5.42
c) Based on the rate in Oct 2020 and assuming a growth rate of g=-0.01 (i.e., rents fall),
what would the resulting ratio NPV/R be? (Again, disregard the fee points)
it’s 2.83%, NPV/P=1/(0.0283+0.01)=26.11