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26 October, 03:45

James wants to be able to make a $30,000 down payment on a new home in three years. If he can invest his savings in an account that earns 6%

interest per year, compounded monthly, about how much will James need to deposit today to achieve his goal?

A.

$25,002

O

B. $25.069

C. $25,189

OD. $35,730

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Answers (1)
  1. 26 October, 03:59
    0
    B. $25,069

    Step-by-step explanation:

    An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.

    If he invests x money what he will have the first month will be:

    Money = x * (1+0.005)

    The next month:

    Money' = Money * (1+0.005) = x * (1+0.005) (1+0.005) = x * (1+0.005) ^2

    Therefore in this type of interest the formula is:

    Money = x * (1+r) ^n

    Where:

    x is the money invested the first time

    r is the interest

    n is the number of periods

    For this problem:

    x = what you have to find

    r = 0.005

    n = 3 years (1 period is 1 month) then the period is 36 months

    Money = 30000

    Replacing:

    30000 = x * (1+0.005) ^36

    x = 25,069
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