Question

show your work

2) A $30,000 construction loan is to be repaid in equal yearly payments over a 10 year period at an effective annual interest rate of 8%. Approximately what percentage of the second payment is applied to the principal? a. 40% b. 50% c. 60% d. 70%

Answer 1

b. 50%

Solution :

Equal annual repayments = loan amount / present value annuity factor at 8%. Where, present value annuity factor =[ 1-(1+r)-n /r] = [1-(1+0.08)-10 /0.08] = [{1-1/(1.08)10}/0.08] = [{1-1/2.15..}/0.08] =[2.15..-1]/0.08 = 6.710 r = rate of interest therefore, Equal annual repayments = 30000/6.71 =$ 4471

In the first year interest = $30000*8% = $2400 In the first year principal = $4471-$2400 = $2071 In the second year interest = ($30000- $2071)*8% =$2234.32 In the second year principal = $4471- $2234.32 = $2236.68 Therefore, Percentage of second payment applied to principal = ($2236.68/$4471)*100 = 50%