Question

Question 1: a) A loan is to be repaid by a student The student has debts of $10,000 to be paid at the end of the first year, $5,000 to be paid in 18 months and $3,000 to be paid in the 24th month The student would prefer to pay the debts as follows. $1,000 now, followed by payments at the end of the 6th, 20th and 30th month. The payment at the end of the 6th month is half the size of the payment at the end of the 20th and 30th months. Find the value of the final repayment (using a focal date of the 30th month) if interest compounds monthly at 8% (5 marks) b) i) For a car loan being repaid with fortnightly installments of $75, find the original loan size if the term of the loan is 5 years, interest is calculated daily at 9%. ii) If the holder of the loan wished to pay out the loan at the end of the 3rd year, how much would be outstanding? ii) In this case (loan paid out in 3 years) what is the total financial fee for this loan? (5 marks)

Answer 1

a) Monthly interest rate=8%/12=0.667%

Value of debt= Present value of 12th, 18th and 24th month's cash flow

=10000/(1+0.667%)^12+5000/(1+0.667%)^18+3000/(1+0.667%)^24=$16226.94

Say, the payment size at the end of 6th month is x. Therefore, the payment size at the end of 20th and 30th month= 2x

So, 1000+x/(1+0.667%)^6+2x/(1+0.667%)^20+2x/(1+0.667%)^30=16226.94

or, x/1.0406+2x/1.1421+2x/1.2205=15226.94

or, x= 3499.973 or 3500(Approx)

Hence, value of 30th payment is $3500.

b) Fortnightly interest rate(rate)=(1+9%/365)^15-1=0.3705%, periodic payment(PMT)=75, nper= 5*12*2=120 fortnight, PV=?

А 1 rate 2 PMT 3 nper 4 PV 0.3705% 75 1201 =PV(B1,B3,B2,0,0) PV(rate, nper, pmt, [fv], [type]) 6

0.3705% Α 1 rate 2 PMT 3 nper 4 PV 75 120 ($7,254.90). -

i) Size of the loan is $7254.90

ii) Below is the amortization schedule of the loan:

O 75 F G Fortnight Original Loarlinterest (G*0.3705%) Repayment Outstanding Loan 0 $7,254.90 $0.00 $7,254.90 1 $7,254.90 $26.88 75 $7,206.78 2 $7,206.78 $26.70 $7,158.48 3 $7,158.48 $26.52 $7,110.00 4 $7,110.00 $26.34 $7,061.34 5 $7,061.34 $26.16 $7,012.51 6 $7,012.51 $25.98 $6,963.49 7 $6,963.49 $25.80 $6,914.29 8 $6,914.29 $25.62 75 $6,864.91 9 $6,864.91 $25.43 75 $6,815.34 10 $6,815.34 $25.25 $6,765.59 11 $6,765.59 $25.07 $6,715.66 12 $6,715.66 $24.88 $6,665.54 13 $6,665.54 $24.70 $6,615.24 14 $6,615.24 $24.51 $6,564.75 15 $6,564.75 $24.32 75 $6,514.07 16 $6,514.07 $24.13 $6,463.20 17 $6,463.20 $23.95 $6,412.15 18 $6,412.15 $23.76 $6,360.91 19 $6,360.91 $23.57 $6,309.47 20 $6,309.47 $23.38 75 $6,257.85 $6,257.85 $23.19 $6,206.04 22 $6,206.04 $22.99 $6,154.03 23 $6,154.03 $22.80 $6,101.83 24 $6,101.83 $22.61 $6,049.44 25 $6,049.44 $22.41 $5,996.85 26 $5,996.85 $22.22 $5,944.07 27 $5,944.07 $22.02 $5,891.09 28 $5,891.09 $21.83 $5,837.92 29 $5,837.92 $21.63 $5,784.55 30 $5,784.55 $21.43 $5,730.98 31 $5,730.98 $21.23 $5,677.21 32 $5,677.21 $21.03 $5,623.25 75 75 75 75 75 75 75 75

75 75 47 75 75 75 55 Fortnight Original Loan Interest (G*0.3705%) Repayment Outstanding Loan 41 $5,184.26 $19.21 $5,128.47 42 $5,128.47 $19.00 $5,072.47 43 $5,072.47 $18.79 $5,016.26 44 $5,016.26 $18.59 $4,959.85 45 $4,959.85 $18.38 $4,903.22 $4,903.22 $18.17 $4,846.39 $4,846.39 $17.96 $4,789.35 48 $4,789.35 $17.74 $4,732.09 49 $4,732.09 $17.53 $4,674.62 50 $4,674.62 $17.32 75 $4,616.94 51 $4,616.94 $17.11 $4,559.05 52 $4,559.05 $16.89 $4,500.94 53 $4,500.94 $16.68 $4,442.62 54 $4,442.62 $16.46 75 $4,384.08 $4,384.08 $16.24 $4,325.32 56 $4,325.32 $16.03 $4,266.35 57 $4,266.35 $15.81 75 $4,207.15 58 $4,207.15 $15.59 $4,147.74 59 $4,147.74 $15.37 $4,088.11 60 $4,088.11 $15.15 $4,028.25 61 $4,028.25 $14.92 $3,968.18 $3,968.18 $14.70 75 $3,907.88 63 $3,907.88 $14.48 $3,847.36 64 $3,847.36 $14.25 $3,786.61 65 $3,786.61 $14.03 $3,725.64 66 $3,725.64 $13.80 $3,664.45 67 $3,664.45 $13.58 $3,603.02 68 $3,603.02 $13.35 $3,541.37 69 $3,541.37 $13.12 $3,479.49 70 $3,479.49 $12.89 $3,417.39 71 $3,417.39 $12.66 $3,355.05 72 $3,355.05 $12.43 $3,292.48 75 75 75

Hence, after 3 year or 3*12*2=72 fortnight outstanding loan amount is $3292,48

iii) Total Interest paid in this case= (75*72+3292.48-7254.9)=$1437.58