Final answer:
The question involves calculating the APR of a mortgage that includes points and origination fees and determining the cost of discount points on a different loan. The APR calculation takes extra costs into account to give a more accurate measure of a loan's cost than the nominal interest rate.
Step-by-step explanation:
The question relates to the calculation of Annual Percentage Rate (APR) for a mortgage loan that includes points and loan origination fees. The APR is a measure of the cost of credit, expressed as a yearly rate, which includes such interest and fees. Since it takes into account these additional fees, the APR provides a more accurate measure of a loan's cost than the simple interest rate.
To find the APR, one would need to know the total cost of these points and fees over the life of the loan and include them in the calculation. For the case of the botanist's loan, this would involve converting the points and origination fee from a percentage to a dollar amount, adding those costs to the loan amount, and then recalculating the effective interest rate given the new total loan cost.
For the other question related to discount points, it's asked to calculate the dollar amount for 3.875 points on a $215,000 loan. Discount points are prepaid interest and are used to lower the interest rate on the loan. To find the cost of the discount points, we would multiply the loan amount by the percentage that each point represents.