 # 1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Loan Repayments Stage 6 - Year 12 General Mathematic (HSC)

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1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Loan Repayments Stage 6 - Year 12 General Mathematic (HSC)

2 { } 2 Loan Repayment (1/2) By thinking of the money borrowed as the Present Value of an annuity we can calculate the Monthly Repayment. M =N r(1+r) n (1+r) n -1 M M is the amount of the monthly repayment. N N is the amount of money borrowed. r r is the rate of interest per period as a decimal. n n is the number of interest periods.

3 { } 3 Loan Repayment (2/2) Georgina has a loan of \$200 000. Her loan is for 30 years with an interest rate of 4.8% p.a. monthly reducible. Find the monthly repayment. M = 200 000 0.004(1+0.004) 360 (1 + 0.004) 360 -1 = 200 000 x (0.004 x 1.004 360 ) (1.004 360 -1) = \$1 049.33 per month { } M =N r(1+r) n (1+r) n -1 Interest per month = 4.8% ÷ 12 = 0.4% Periods= 30y x 12m = 360 = 0.004

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