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2 November, 16:25

You are saving to buy a $185,000 house. There are two competing banks in your area, both offering certificates of deposit yielding 7 percent.

How long will it take your initial $102,000 investment to reach the desired level at First Bank, which pays simple interest? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Number of years

How long will it take your initial $102,000 investment to reach the desired level at Second Bank, which compounds interest monthly? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

Number of years

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  1. 2 November, 16:51
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    (1) First Bank pay simple interest, number of year is 11.62 years

    (2) Second Bank pay compound interest, number of year is 8.8 years

    Explanation:

    Future value (FV) : $185,000

    Rate: 7% per annual

    Present value (PV) : $102,000

    Total interest required to have enough morning to buy a house = $185,000 - $102,000 = $83,000

    (1) First Bank pay simple interest:

    $83,000 = $102,000 * 7% * number of years

    => Number of years = $83,000 / ($102,000 * 7%) = 11.62 years

    (2) Second Bank pay compound interest:

    $83,000 = $102,000 * (1+7%) ^number of years - $102,000

    => (1+7%) ^number of years = ($83,000+$102,000) / $102,000

    ⇔ (1.07) ^number of years = 1.8137

    => Number of years = log (1.8137, 1.07) = 8.8 years
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