Question

2. Irene and Frank Adam plan to purchase an 80 acre tract of land valued at $2,200 per acre. The lender charges a $500 loan application fee and $250 for a real estate appraisal. A stock requirement of 5% of the loan amount (after addition of fees) is required. The fees and stock requirement can be added to the original loan amount. The original stock value will be returned upon retiring the loan. The contractual rate is 8%. The fixed annual payments are based on a 20 year amortization period. The interest is calculated using the remaining balance method.

a. What is the effective annual interest rate for the loan?

b. What is the effective annual interest rate for the loan if there is no stock requirement? c. What is the effective annual interest rate if the amortization period is lengthened to 30 years using the conditions of question a? Explain the difference from the answer in a.

Answer 1

According to the above given question the solution as follows :

The credit sum required = $2200 per section of land * 80 sections of land = $176,000

Expenses = $500+$250 = $750

Aggregate sum for stock prerequisite =$176,750

Stock prerequisite =$176750*5%=$8837.50 which will be discharged upon last installment

Aggregate sum on which intrigue is charged = $176750+$8837.50 = $185587.50

In this way, A/0.08*(1-1/1.08^20) = 185587.50 where An is yearly installment

=> A = $18902.50

an) Annual Effective rate (r) is given by

18902.50/r*(1-1/(1+r)^20)- 8837.50/(1+r)^20 = 176000

r = 0.085+ (177151.93-176000)/(177151.93-175888.41)*(0.086-0.085) =0.085912

So,effective yearly financing cost for the advance is 8.59% (Correct to three decimal spots).

b) If there is no stock necessity

Thus, A/0.08*(1-1/1.08^20) = 176750 where An is yearly installment

=> A = $18002.38

Yearly Effective rate (r) is given by

18002.38/r*(1-1/(1+r)^20) = 176000

r = 0.0805+ (176094.28-176000)/(176094.28-175442.41)*(0.081-0.0805) =0.080572

So,effective yearly financing cost for the credit is 8.057% (Correct to three decimal spots).

c)If amortization period is reached out to 30 years

In this way, A/0.08*(1-1/1.08^30) = 185587.50 where An is yearly installment

=> A = $16485.26

an) Annual Effective rate (r) is given by

16485.26/r*(1-1/(1+r)^30)- 8837.50/(1+r)^30 = 176000

r = 0.085+ (176399.92-176000)/(176399.92-174812)*(0.086-0.085) =0.085252

So,effective yearly financing cost for the credit is 8.525% (Correct to three decimal spots).