Question

A design studio received a loan of $9,650 at 4.60% compounded semi-annually to purchase a camera. If they settled the loan in 3 years by making quarterly payments, construct the amortization schedule for the loan and answer the following questions: a. What was the payment size? Round to the nearest cent b. What was the size of the interest portion on the first payment? Round to the nearest cent c. What was the balance of the loan at end of the first year?

Answer 1

a) The payment size was $ 865.18

b) The size of interest portion on the first payment $ 110.34

c) The balance of the loan at end of the first year $ 8895.16

d) The interest portion on the last payment $ 9.78

Please refer to below images on calculation part

4.60% Given Given semi annually Yearly Nominal Rate(R) Compounding frequency Times compounded a year EAR=((1+R/t)^t)-1 2 4.6529 % ((1+F7/F9)^F9)-1 Quaterly Frequency Times compoudning a year Quaterly rate Yearly rate(Quarterly compounding) ((1+F10/100)^(1/F13)-1)*100 F14* F13 4 1.143462468 % 4.573849872 %

Quaterly payments Equated quarterly payment is calculated using EQI=[P*r*(1+r)^n]/[(1+r)^n)-1 Where P=Principal;n=Number of installments;r = rate of interest per quarter in decimals All Amounts in $ 9650 Number of years N 4.573849872 Number of quarters n Principal P Rate of interesr R %p.a) 3 12 Interest rate per quarter No of quarters (n) R/(100*4) N*4 (1+r) (1+r)^n (1+r)^n-1 P*r*(1+r)^n [P*r*(1+r)^n]/[(1+r)^n)-1 E24/(100*4) G23*4 1+G26 G28^G27 G29-1 E23*G26*G29 G31/G30 Rounded to nearest cent($) 0.011434625 12 1.011434625 1.146182576 0.146182576 126.4745171 865.1818857 865.18 Amortization Schedule

Quarter Beginning Balance 1 2 3 4 5 Amortization Schedule Quarterly interest Quarterly Payment Interest Component Principal Component End Balance 9650 0.011434625 865.18 110.34 754.84 8895.16 8895.16 0.011434625 865.18 101.71 763.47 8131.69 8131.69 0.011434625 865.18 92.98 772.2 7359.49 7359.49 0.011434625 865.18 84.15 781.03 6578.46 6578.46 0.011434625 865.18 75.22 789.96 5788.5 5788.5 0.011434625 865.18 66.19 798.99 4989.51 4989.51 0.011434625 865.18 57.05 808.13 4181.38 4181.38 0.011434625 865.18 47.81 817.37 3364.01 3364.01 0.011434625 865.18 38.47 826.71 2537.3 2537.3 0.011434625 865.18 29.01 836.17 1701.13 1701.13 0.011434625 865.18 19.45 845.73 855.4 855.4 0.011434625 865.18 9.78 855.4 0 6 7 8 9 10 11 12