Question

Ms. Suzuki invested $14,000 in two accounts, one yielding 8% interest and the other yielding 10%. If she received a total of $1,220 in interest at the end of the year, how much did she invest in each account?

a) $6,000 at 8%, $8,000 at 10%
b) $8,000 at 8%, $6,000 at 10%
c) $7,000 at 8%, $7,000 at 10%
d) $9,000 at 8%, $5,000 at 10%

Answer 1

Ms. Suzuki invested $9,000 at 8% and $5,000 at 10%. This was determined by setting up a system of equations based on the total amount invested and the total interest earned, then solving for the amounts in each account.

Step-by-step explanation:

Ms. Suzuki invested $14,000 in two different interest-bearing accounts, one at 8% annual interest and the other at 10% annual interest. She received a total of $1,220 in interest at the end of the year. To determine how much she invested in each account, we can set up a system of equations:

• Let x be the amount invested at 8%.
• Let y be the amount invested at 10%.

The total amount invested is $14,000, which leads to our first equation: x + y = 14,000

The total interest from both accounts is $1,220, leading to our second equation based on the interest rates: 0.08x + 0.10y = 1,220

Solving these simultaneous equations, we start by multiplying the second equation by 100 to clear the decimals: 8x + 10y = 122,000

Next, we can multiply the first equation by 8 to help eliminate a variable: 8x + 8y = 112,000

Subtracting the fourth equation from the third gives us: 2y = 10,000

Dividing through by 2, we find that y = $5,000. Substituting y into the first equation x + 5,000 = 14,000 gives us x = $9,000.

Thus, Ms. Suzuki invested $9,000 at 8% and $5,000 at 10%.

Answer choice (d) is correct.