Question

# Nicola borrows a \$24000 loan from Steve. She agrees to pay interest on the loan at...

Nicola borrows a \$24000 loan from Steve. She agrees to pay interest on the loan at the end of each year for 8 years, and will repay the capital by accumulation of a sinking fund. The sinking fund deposits are such that the net amount of the loan decreases linearly, resulting in a level repayment of principal at the end of each year. The interest rate on the loan is 5% over the first 4 years and 4.5% over the next 4 years. The sinking fund earns a fixed 4% interest rate per annum.

(a) Find the total amount of the 5th installment paid by Nicola. (Ans. \$3600)

(b) Compare this with the case when Nicola repays the loan with 8 equal annual installments.

Principle amount repayment/year will be=24000/8=3000/yr

 Year Amount o/s Interest(5%/4.5% Total Repayment amount Balance 1 24000 1200 25200 4200 21000 2 21000 1050 22050 4050 18000 3 18000 900 18900 3900 15000 4 15000 750 15750 3750 12000 5 12000 540 12540 3540 9000 6 9000 405 9405 3405 6000 7 6000 270 6270 3270 3000 8 3000 135 3135 3135 0 Total 29250

b) when Nicola repays the loan with 8 equal annual installments.=29250/8=3656.25/installment

Difference between two=3656.25-3540=116.25

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