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Compound Interest/Future Value2020-12-30T22:03:08+10:00

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    Keymaster
    December 4, 2018 at 5:16 pm
    Post count: 1622
    #15266
    Compound Interest/Future Value

    FV =PV(1 + r)n

    FV = Future Value
    PV = Present Value

    A = P(1 + r)n

    A = total of principal and interest
    P = principal, original amount borrowed or invested
    r = interest rate as a decimal ie. divide the percent by a hundred
    n = length of the loan or investment

    Admin
    Keymaster
    December 30, 2020 at 10:04 pm
    Post count: 1622
    #18592

    How long will it take an investment of $10 000 to double at an interest rate of 7.5% p.a. compounded monthly?

    20 000 = 10 000(1 + 0.00625)n
    2 = (1 + 0.00625)n

    then start ‘guessing and checking’ values for n to make it work

    n = 100: (1 + 0.00625)100 = 1.86 too low
    n = 150: (1 + 0.00625)150 = 2.54 too high
    n = 125: (1 + 0.00625)125 = 2.17 too high
    n = 115: (1 + 0.00625)115 = 2.04 too high
    n = 110: (1 + 0.00625)110 = 1.98 too low
    n = 111: (1 + 0.00625)111 = 1.997 too low
    n = 112: (1 + 0.00625)112 = 2.00 too low

    n = 112 months

    $$\frac{112}{12}$$
    = 9.3 years

    Admin
    Keymaster
    December 30, 2020 at 10:05 pm
    Post count: 1622
    #18593
    Find the amount $1000 amounts to if it is invested at 10% pa compounded annually for 5 years.
    A = 1000(1 + 0.1)5 10% = 10 ÷ 100 = 0.1 as a decimal, r = 0.1, n = 5, P = 1000
    A = $1610.51 calculate
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    Keymaster
    December 30, 2020 at 10:06 pm
    Post count: 1622
    #18594
    Find the amount $1000 amounts to if it is invested at 12% pa compounded monthly for 5 years.
    A = 1000(1.01)60
    A = $1816.70

    Be careful of the time periods here. We need to change 12% pa into per month so we divide by 12 to get 1% per month.
    And we need to change 5 years into months by multiplying by 12 to get 60 months.

    r = 0.01, n = 60, P = 1000
    Admin
    Keymaster
    December 30, 2020 at 10:07 pm
    Post count: 1622
    #18595
    Find the amount of interest on $6000 if it is invested at 8% pa, for ten years, compounded quarterly.
    A = 6000(1.02)40
    A = $13248.24    		 8% pa is 8 ÷ 4 = 2% per quarter and ten years is 10 × 4 = 40 quarters
    P = 6000, r = 0.02, n = 40
    ∴ the interest will be $13248.24 – $6000
    = $7248.24    		 A is the amount of the investment = principle + interest, so to find the interest, take the original investment away from the total amount
    Admin
    Keymaster
    December 30, 2020 at 10:11 pm
    Post count: 1622
    #18596
    What amount of principal must be invested at 5.8% pa for it to grow to $15 000 in 8 years if:
    a. Simple interest applies? answer to the nearest cent
    b. Compound interest applies? answer to the nearest cent

    a. P + (P × 5.8% × 8) = 15 000

    P + (P × 0.058 × 8) = 15 000

    P + 0.464P = 15 000

    1.464P = 15 000

    $$\frac{\cancel{1.464}P}{\cancel{1.464}}=\frac{15,000}{1.46}$$
    P = $10 245.90164

    ∴ $10,245.90

    		 let the principle be P
    interest = PRN
    Interest + Principle = $15 000
    PRN + P = 15 000
    form an equation and use it to solve for P

    b. 15000 = P(1+ 0.058)8

    15000 = P(1.058)8

    $$\frac{{15,000}}{{{{(1.058)}^8}}} = \frac{{P{{\cancel{(1.058)}^8}}}}{{{{\cancel{(1.058)}^8}}}}$$

    P = $9554.4595959

    ∴ $9554.46

    A = P(1 + r)n

    where P is unknown, r = 0.058, n = 8

    solve the equation for P
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