"Investment" Word Problems: Examples (page 2 of 2)

If you set up your investment word problems so everything is labeled and well-organized, they should all work out fairly easily. Just take your time and do things in an orderly fashion. I've done the set-up (but not the complete solutions) for a few more examples:

• An investment of \$3,000 is made at an annual simple interest rate of 5%. How much additional money must be invested at an annual simple interest rate of 9% so that the total annual interest earned is 7.5% of the total investment?

 I P r t first (3,000)(0.05) = 150 3,000 0.05 1 additional 0.09 x x 0.09 1 total (3,000 + x)(0.075) 3,000 + x 0.075 1

First I fill in the P, r, and t columns with the given values.

Then I multiply across the rows (from the right to the left) in order to fill in the I column.

Then add down the I column to get the equation 150 + 0.09 x = (3,000 + x)(0.075).

To find the solution, I would solve for the value of x.

• A total of \$6,000 is invested into two simple interest accounts. The annual simple interest rate on one account is 9%; on the second account, the annual simple interest rate is 6%. How much should be invested in each account so that both accounts earn the same amount of annual interest?

 I P r t 9% account 0.09x x 0.09 1 6% account (6,000 – x)(0.06) 6,000 – x 0.06 1 total --- 6,000 --- ---

In this problem, I don't actually need the "total" row at all.

First I'll fill in the P, r, and t columns, and multiply to the left to fill in the I column.

From the interest column, I then get the equation 0.09x = (\$6,000 – x)(0.06), because the yields are required to be equal.

Then I'd solve for the value of x, and back-solve to find the value invested in the 6% account.

(This exercise's set-up used that "how much is left" construction, mentioned earlier.)

• An investor deposited an amount of money into a high-yield mutual fund that returns a 9% annual simple interest rate. A second deposit, \$2,500 more than the first, was placed in a certificate of deposit that returns a 5% annual simple interest rate. The total interest earned on both investments for one year was \$475. How much money was deposited in the mutual fund?
• The amount invested in the CD is defined in terms of the amount invested in the mutual fund,so I will let "x" be the amount invested in the mutual fund.

 I P r t mutual fund 0.09x x 0.09 1 cert. of deposit (x + 2,500)(0.05) x + \$2,500 0.05 1 total 475 2x + \$2,500 --- ---

In this problem, I don't actually need the "total" for the "rate" or "time" columns.

First I'll fill in the P, r, and t columns, multiplying to the left to fill in the I column.

Then I'll add down the I column to get the equation 0.09x + (x + 2,500)(0.05) = 475.

• The manager of a mutual fund placed 30% of the fund's available cash in a 6% simple interest account, 25% in 8% corporate bonds, and the remainder in a money market fund that earns 7.5% annual simple interest. The total annual interest from the investments was \$35,875. What was the total amount invested?
• For this problem, I'll let "x" stand for the total amount invested.

 I P r t 6% account (0.30x)(0.06) = 0.018x 0.30x 0.06 1 8% bonds (0.25x)(0.08) = 0.02x 0.25x 0.08 1 7.5% fund (0.45x)(0.075) = 0.03375x 0.45x 0.075 1 total \$35,875 x --- ---

Once 30% and 25% was accounted for in the 6% and 8% accounts, then there is 100% – 30% – 25% = 45% left for the third account. I can use this information to fill in the "principal" column.

Then I'll fill out the "rate" and "time" columns, and multiply to the left to fill in the "interest" column.

From the interest column, I get the equation 0.018x + 0.02x + 0.03375x = 35,875.

Then I'd solve for the value of x.