Problem 6-62 Calculating EAR with Points [LO4] You are looking at a one-year loa

Question

Problem 6-62 Calculating EAR with Points [LO4] You are looking at a one-year loan of $14,500. The interest rate is quoted as 9.9 percent plus three points. A point on a loan is 1 percent (one percentage point) of the loan amount. Quotes similar to this one are common with home mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the loan later with 9.9 percent interest. What rate would you actually be paying here? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Interest rate 0

Explanation / Answer

6-62

PV of the loan = 14500

Interest to be paid now= 3%*14500 = 435

Updated PV= 14500-435 = $14065

FV of the loan = PV*(1+r)^n

=14500*(1+0.099)

=15935.5

FV=PV*(1+r)^n

15935.5=14065 *(1+r)^1

1+r= 1.13299

R= 13.3%

6-50

PV of the perpetuity = Annuity/rate

= 3800/5.4% = 70370.3704

This occurs at time 20

PV of this perpetuity at t=10 = Fv/(1+r)^n

= 70370.37/ 1.054^10

=41589.5

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