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Math Help - another annuity

  1. #1
    Senior Member euclid2's Avatar
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    another annuity

    1. You wish to purchased a house for $120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years)
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  2. #2
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    another annuity

    Quote Originally Posted by euclid2 View Post
    1. You wish to purchased a house for $120,000 in 12 years. You can invest your money at 4.5%/a compounded semiannually for the first 5 years and then you can get 6%/a compounded semiannually for the next 7 years. How much do you need to invest now? (Hint: start with the last 7 years)
    For the last seven years,

    interest, i = \frac{6}{2}\%=3\%=0.03

    number of interest periods, n = 7 \times 2 = 14

    The value of investment at the end of first five years

    = \frac {120 000}{(1.03)^{14}}

    = \$79 334.14


    For the first five years,

    interest, i = \frac{4.5}{2}\%=2.25\%=0.0225

    number of interest periods, n = 5 \times 2 = 10

    The present value of investment is

    = \frac {\$79 334.14}{(1.0225)^{10}}

    = \$63 507.78
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