Question

Dillon plans to invest $16,000 part at 4% simple interest and the rest at 5% simple interest what is the most he can invest at 4% and still be guaranteed at least 700 per year

Answer 1

Answer:

Step-by-step explanation:

The simple interest formula is P * r * t = I, where P is the initial investment, r is the interest rate in decimal form, t is the time in years.  This problem would be best solved by making a table, one row for account 1 and one row for account 2 with the formula along the top:

              P     *     r     *     t     =     I

acct 1

acct 2

First let's fill in our years.  The words "per year" were used, so the time in each row is a 1:

            P     *      r      *      t       =      I

acct 1                                 1

acct 2                                1

Now let's fill in the interest rates as decimals:

         P     *     r     *     t     =     I

acct 1            .04          1

acct 2           .05          1

Now for the principle amount.  If all we have to invest is 16000 and we put x into one account, then all we have left to put into the other account is what's left after taking x out of 16000, or 16000 - x.

                     P      *      r      *      t      =      I

acct 1             x           .04           1

acct 2   16000 - x       .05          1

The formula tells us that we multiply the P times the r times the t to get I, so lets do that.  Multiply straight across the top to get an interest of .04x.  Multiply straight across the bottom to get an interest of .05(16000 - x) which, after distributing, is 800 - .05x:

                 P      *      r      *      t      =      I

acct 1         x           .04            1      =    .04x

acct 2   16000-x    .05            1      =   800 - .05x

We need the amount of interest that we earn from both of these accounts to equal 700, so add the last column and set it equal to 700:

.04x + 800 - .05x = 700.  Combine like terms to get

-.01x = -100 so

x = 10,000

That means that the account which has an interest rate of 4% can have 10,000 in it while the other account has 6,000 in it.