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Compound InterestStage 6 - Year 11

Applied Mathematic(Preliminary General 1)

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When do we use compound interest?

Savings Accounts

Interest can be calculated …

AnnuallySix-monthly

Quarterly

Monthly

Daily

÷2

÷4

÷12

÷365.25

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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

= 0.08

= 0.08

= 0.08

÷4

÷12

÷365.25

= 0.04

= 0.02

= 0.006.

= 0.000219…

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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

= 0.04

= 0.04

= 0.04

÷4

÷12

÷365.25

= 0.02

= 0.01

= 0.003.

= 0.000109…

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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.

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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 +0.07)2

= $50 000x 1.072

= $57 245.00I = $57 245.00 - $50 000

= $7 245.00

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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 +0.035)4

= $50 000x 1.0354

= $57 376.15

r = 0.07 ÷ 2= 0.035

n = 2yr x 2= 4 periods

I = $57 376.15 - $50 000= $7 376.15

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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 +0.0175)8

= $50 000x 1.01758

= $57 444.09

r = 0.07 ÷ 4= 0.0175

n = 2yr x 4= 8 periods

I = $57 444.09 - $50 000= $7 444.09

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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 +0.00583)24

= $50 000x 1.0058324

= $57 485.54

r = 0.07 ÷ 12≈ 0.00583

n = 2yr x 12= 24 periods

I = $57 485.54 - $50 000= $7 485.54

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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 +0.000192)730.5

= $50 000x 1.000192730.5

= $57 527.64

r=0.07÷365.25

≈ 0.000192

n =2yr x 365.25

=730.5 periodsI = $57 527.64 - $50 000

= $7 527.64

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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

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Table for $1

A = P (1+ r)n

1 2 3 4 5 6 7 8 9 105% 1.05 1.10 1.16 1.22 1.28 1.34 1.41 1.48 1.55 1.63

6% 1.06 1.12 1.19 1.26 1.34 1.42 1.50 1.59 1.69 1.79

7% 1.07 1.14 1.23 1.31 1.40 1.50 1.61 1.72 1.84 1.97

8% 1.08 1.17 1.26 1.36 1.47 1.59 1.71 1.85 2.00 2.16

PeriodsPeriods

Inte

rest

Inte

rest

A = 5000 x1.84= $9,200

$5000@ 7%

9 years

Tables can make it easier

I = 9200 - 5000= $4,200

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Table for $1

A = P (1+ r)n

1 2 3 4 5 6 7 8 9 105% 1.05 1.10 1.16 1.22 1.28 1.34 1.41 1.48 1.55 1.63

6% 1.06 1.12 1.19 1.26 1.34 1.42 1.50 1.59 1.69 1.79

7% 1.07 1.14 1.23 1.31 1.40 1.50 1.61 1.72 1.84 1.97

8% 1.08 1.17 1.26 1.36 1.47 1.59 1.71 1.85 2.00 2.16

PeriodsPeriods

Inte

rest

Inte

rest

A = 250 x 1.41= $352.50

$250@ 5%pa7 years

Tables can make it easier

I = 352.50 - 250= $102.50