# 1 Press Ctrl-A ©G Dear2010 – Not to be sold/Free to use Compound Interest Stage 6 - Year 11 Applied Mathematic (Preliminary General 1)

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1 Press Ctrl-A ©G Dear2010 – Not to be sold/Free to use Compound Interest Stage 6 - Year 11 Applied Mathematic (Preliminary General 1)

2 When do we use compound interest? Savings Accounts Interest can be calculated … Annually Six-monthly Quarterly Monthly Daily ÷2 ÷4 ÷12 ÷365.25

3 For an annual interest rate of 8% find the… Annually rate Six-monthly rate Quarterly rate Monthly rate Daily rate ÷2 = 0.08 (as a decimal) = 0.08 ÷4 ÷12 ÷365.25 = 0.04 = 0.02 = 0.006. = 0.000219…

4 For an annual interest rate of 4% find the… Annual rate Six-monthly rate Quarterly rate Monthly rate Daily rate ÷2 = 0.04 (as a decimal) = 0.04 ÷4 ÷12 ÷365.25 = 0.02 = 0.01 = 0.003. = 0.000109…

5 The Formula A = P (1+ r) n A = Future Value or Annuity P = Principal (Money) r = Rate of Interest as a decimal. n = Number of Interest Periods.

6 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 years at 7% p.a. calculated annually… A = \$50 000( 1 +( 1 +0.07) 2 = \$50 000x 1.07 2 = \$57 245.00 I = \$57 245.00 - \$50 000 = \$7 245.00

7 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 years at 7% p.a. calculated six-monthly… A = \$50 000( 1 +( 1 +0.035) 4 = \$50 000x 1.035 4 = \$57 376.15 r = 0.07 ÷ 2 = 0.035 n = 2yr x 2 = 4 periods I = \$57 376.15 - \$50 000 = \$7 376.15

8 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 year2 at 7% p.a. calculated quarterly… A = \$50 000( 1 +( 1 +0.0175) 8 = \$50 000x 1.0175 8 = \$57 444.09 r = 0.07 ÷ 4 = 0.0175 n = 2yr x 4 = 8 periods I = \$57 444.09 - \$50 000 = \$7 444.09

9 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 years at 7% p.a. calculated monthly… A = \$50 000( 1 +( 1 +0.00583) 24 = \$50 000x 1.00583 24 = \$57 485.54 r = 0.07 ÷ 12 ≈ 0.00583 n = 2yr x 12 = 24 periods I = \$57 485.54 - \$50 000 = \$7 485.54

10 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 years at 7% p.a. calculated daily… A = \$50 000( 1 +( 1 +0.000192) 730.5 = \$50 000x 1.000192 730.5 = \$57 527.64 r =0.07÷365.25 ≈ 0.000192 n =2yr x 365.25 =730.5 periods I = \$57 527.64 - \$50 000 = \$7 527.64

11 A = P (1+ r) n Samantha has \$50000 and invests it at St George Bank for 2 years at 7% p.a. Calculated Annually = \$7 245.00 Six-monthly = \$7 376.15 Quarterly = \$7 444.09 Monthly = \$7 485.54 Daily = \$7 527.64 ? Interest

12 Table for \$1 A = P (1+ r) n 12345678910 5% 1.051.101.161.221.281.341.411.481.551.63 6% 1.061.121.191.261.341.421.501.591.691.79 7% 1.071.141.231.311.401.501.611.721.841.97 8% 1.081.171.261.361.471.591.711.852.002.16 Periods Interest A = 5000 x1.84 = \$9,200 \$5000 @ 7% 9 years Tables can make it easier I = 9200 - 5000 = \$4,200

13 Table for \$1 A = P (1+ r) n 12345678910 5% 1.051.101.161.221.281.341.411.481.551.63 6% 1.061.121.191.261.341.421.501.591.691.79 7% 1.071.141.231.311.401.501.611.721.841.97 8% 1.081.171.261.361.471.591.711.852.002.16 Periods Interest A = 250 x1.41 = \$352.50 \$250 @ 5%pa 7 years Tables can make it easier I = 352.50 - 250 = \$102.50

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