Question

A loan at 7% annually has an initial payment of 250, and 9 further payments. The payment amount increases by 3% each year. Find the loan balance immediately after the 7th payment.

Answer 1

A B C D E F G H I J K L WN Repayment 250 257.50 265.23 273.18 281.38 289.82 11 000 O 298.51 307.47 316.69 326.19 13 The last instalment amount is $326.19, this includes balance of principal to be repaid Plus interest on the balance amount. Loan amount principal in the last EMI = $326.19*100/107 = $304.85 Opening principal outstanding+ interest =Repayment+Closing principal outstading. Let x be opening principal outstainding. Interest would be 7% of x (0.07x). Therefore for the 9th month Repayment+ closing principal outstanding =$621.55 it means 1.07x =$621.55 x=$621.55/1.07 x=$580.887. interest =$40.66.

Year 10 8 7 Opening Principal outstanding $304.85 $580.88 $830.24 $1,054.91 $1,256.75 $1,437.50 $1,598.77 $1,742.05 $1,868.74 $1,980.13 Closing Interest Repayment Principal outstanding $21.34 $326.19 $0.00 $40.66 $316.69 $304.85 $58.12 $307.47 $580.88 $73.84 $298.51 $830.24 $87.97 $289.82 $1,054.91 $100.63 $281.38 $1,256.75 $111.91 $273.18 $1,437.50 $121.94 $265.23 $1,598.77 $130.81 $257.50 $1,742.05 $138.61 | $250.00 $1,868.74 2 From the above schedule Principal outstanding after the payment of 7th instalment is $830.24. 43

Excel formula:

Yea Repayment 250 C5*(1+0.03) =C6*(1+0.03) =C7*(1+0.03) =C8*(1+0.03) =C9*(1+0.03) =C10*(1+0.03) =C11*(1+0.03) =C12*(1+0.03) =C13*(1+0.03) 11 12 13 14 15