Question

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ind 9% The debt is amortized by the periodic payment shown. Compute (a) the number of payments required to amortize the debt; (b) the outstanding principal at the time indicated. Payment Conversion Outstanding Debt Principal Debt Payment Interval Interest Rate Period Principal After: $15,000 $1483 1 month monthly 8th payment (a) The number of payments required to amortize the debt is (Round the final answer up to the nearest whole number. Round all intermediate values to six decimal places as needed.) (b) The outstanding principal is $. (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Answer 1

Solution:  The formula used to calculate when the debt is amortized by a periodic payment is given below:

  

R= Pi 1-(1+i)"

Here R is debt payment which is given in question = $1483

Here P is debt principal which is given in question = $15000

9 Herei is interest rate/12 which is given in question 0.09 12 100 x 12

n is time in months

(a)The solution is given below:

Pi 1-(1+ tn Putting all values in above calculate formulas Murboso of payments 1983 15000 Gaxios - (1 + 19X100 in time in months 9 M Here, 15 000 (0.0075 (20075 )- 1483 12.5 1 -- (1.0075) -M 1- (1.0075) - 1483 00075) = 0.075859 0.075859 = 0.0075 - 0.929140 (1.0075) Take long on both sides Log 0.924040 -Me log 0.0075) -0.03426 = M X 0.003295 Q:03426 10:557781 0.003245

n = 10.557781= 11 months

(b) The solution is given below:

Outstanding payment after 8 months = Payment after 11 months - Payment after 8 months= Payment for 3 months

Outstanding payment after 8 months = P₁₁ - P₈ = P₃

_{8th Outstanding Principale Pil - Po after B. B [1o-(1+i) - Rz Outstanding Principal 1483 [1-CI+ ) 1403 [ 12 (1+0.0075) 3 0.0075 1483 (1.0075)-3] 0.0075 1483 [1 - 0.977833 0.0075 1483 X 0.022166 0.0075 32.873174 0.0075 $4383.0899) Answer $ 438.3}

Answer :

(a) Number of payments required to amortize the debt = 11 months

(b) Outstanding payment after 8 months = $4383