Business Mathematics 5 types of transactions / questions Simple Interest – flat rate of interest Compound Interest – invest a single amount and see what it will grow to – PV Present value grows to FV Future Value Compound Interest – the reciprocal of (2) above – someone promises to give you a single amount at a future date FV – what is it’s value today – PV – present value Compound Interest – Deposit a regular amount – annuity and see what it will grow to FV Compound Interest – Receive a single amount today (Loan) what future income payments will be the equivalent of this loan amount OR Invest a single amount today what future income stream (annuity) should I expect to receive from this investment

Another way of expressing the above calculation in words is : How much would I need to invest today to receive a regular payment of $1500 for the next 8 years if the annual interest rate was 13% ? The answer is $7198.16. How much interest have I earned ? 1500 x 8 = 12000 – 7198.16 = $4801

Proof Opening Interest Less Closing Balance at 13% Payment 1 $7,198.16 $ 935.76 $ 1,500.00 $ 6,633.92 2 $6,633.92 $ 862.41 $ 5,996.33 3 $5,996.33 $ 779.52 $ 5,275.85 4 $5,275.85 $ 685.86 $ 4,461.71 5 $4,461.71 $ 580.02 $ 3,541.74 6 $3,541.74 $ 460.43 $ 2,502.16 7 $2,502.16 $ 325.28 $ 1,327.44 8 $1,327.44 $ 172.57 $ 0.01 Total $ 4,801.85

Below is the first 12 months of the 8 year loan Opening Interest Less Closing Balance at 9% Payment 1 $ 50,000.00 $ 375.00 $ 732.51 $ 49,642.49 2 $ 372.32 $ 49,282.30 3 $ 369.62 $ 48,919.41 4 $ 366.90 $ 48,553.79 5 $ 364.15 $ 48,185.43 6 $ 361.39 $ 47,814.32 7 $ 358.61 $ 47,440.41 8 $ 355.80 $ 47,063.71 9 $ 352.98 $ 733.51 $ 46,683.17 10 $ 350.12 $ 734.51 $ 46,298.79 11 $ 347.24 $ 735.51 $ 45,910.52 12 $ 344.33 $ 736.51 $ 45,518.34

Below is the last 12 months of the 8 year loan 85 $ 8,376.21 $ 62.82 $ 732.51 $ 7,706.52 86 $ 57.80 $ 7,031.81 87 $ 52.74 $ 6,352.04 88 $ 47.64 $ 5,667.17 89 $ 42.50 $ 4,977.16 90 $ 37.33 $ 4,281.98 91 $ 32.11 $ 3,581.59 92 $ 26.86 $ 2,875.94 93 $ 21.57 $ 2,165.00 94 $ 16.24 $ 1,448.72 95 $ 10.87 $ 727.08 96 $ 5.45 $ 0.02

This is saying how much would I need to invest to receive $100 per month for the next 12 months if I could invest at 12% per annum compounding monthly? Answer $1125.51 How much interest have I earned? 100 x 12 = 1200 – 1125.51 = $74.49

Opening Interest Less Closing Balance at 12% Payment 1 $ 1,125.51 $ 11.26 $ 100.00 $ 1,036.77 2 $ 10.37 $ 947.13 3 $ 9.47 $ 856.60 4 $ 8.57 $ 765.17 5 $ 7.65 $ 672.82 6 $ 6.73 $ 579.55 7 $ 5.80 $ 485.35 8 $ 4.85 $ 390.20 9 $ 3.90 $ 294.10 10 $ 2.94 $ 197.04 11 $ 1.97 $ 99.01 12 $ 0.99 $ 0.00 $ 74.49

Old Financial Calculator New Financial Calculator AMRT, 3, ENT, (P1 set to 3), down arrow (to set P2 to 3 as well ), 3, ENT, then keep pressing scroll down to check Principal, Interest and Balance,….. Keep scrolling to AMRT P1 – change to 4, ENT then scroll down to P2 and change this to 4 as well – (4, ENT) – this will give the interest component and principal component after the 4th payment

Practice the AMRT button for other loan schedule lines For example Keep scrolling to AMRT P1 – change to 1, ENT then scroll down to P2 and change this to 1 as well – (1, ENT) – this will give the interest component and principal component after the 1st payment Now scroll to AMRT P1 – change to 1, ENT then scroll down to P2 and change this to 5 – (5, ENT) – this will give the interest component and principal component after all 5 payments – that is total paid off the principal is $5000, and total interest paid is $1935.24

AMRT, 3, ENT, (Scroll Down to AMRT P2=)… AMRT, 3, ENT, (Scroll Down to AMRT P2=)…. 3, ENT, Scroll Down – Balance to pay out the loan is….. $38,355.92

(d) At the end of the sixth year just prior to the instalment due at that time So we have 6 x 12 = 72, so we have made 71 payments – AMRT, 72, ENT, Scroll down to P2 , 72, ENT, then scroll down and find the balance payable would be $112472.62 but just prior to the payment due means we still owe the 12th payment for that year to pay out the loan – 112472.62 plus 3421.64 = $115893 See the snap shot of the loan schedule below and see if you agree that the logic is correct…….if the question had said immediately after the last payment of the sixth year then the payout figure would be $112,472.62, but just before the last payment means we owe $112,472.62 plus one more repayment. To Reconcile this $115893 – interest for the 72nd payment = 115317.67 68 $ 126,557.04 $ 632.79 $ 3,421.64 $ 123,768.18 69 $ 123,768.18 $ 618.84 $ 120,965.38 70 $ 120,965.38 $ 604.83 $ 118,148.57 71 $ 118,148.57 $ 590.74 $ 115,317.67 72 $ 115,317.67 $ 576.59 $ 112,472.62 73 $ 112,472.62 $ 562.36 $ 109,613.35