Monica decided to divide a total of $42,000 into three investments: a savings account paying 5% interest, a time deposit paying 7%, and a bond paying 9%

Question

Monica decided to divide a total of $42,000 into three investments: a savings account paying 5% interest, a time deposit paying 7%, and a bond paying 9%. Her total annual interest from the three investments was $2600, and the interest from the savings account was $200 less than the total interest from the other two investments. How much did she invest at each rate?

Invested in savings = $

Invested in stocks = $

Invested in mutual funds = $

Answer 1

s = savings, d = time deposit, b = bond paying

 

s + d + b = 42000 eq. 1 (Total investment is the sum of all individual investment)

 

.05s + .07d + .09b = 2600 eq. 2 (Total interest is the sum of all individual interest I = Prt, with t = 1 [annual])

 

.05s = (.07d + .09b) - 200 eq. 3

 

 

Do elimination with eq. 2 and tweaked eq. 3:

 

.05s + .07d + .09b = 2600

.05s  - .07d  - .09b = - 200

 

.1s + 0 + 0 = 2400; s = 24000

 

Substitute s to eq. 1 and either eq. 2 or 3. Let me use 1 and 2:

 

24000 + d + b = 42000

 

d + b = 18000 eq. 4

 

.05(24000) + .07d + .09b = 2600

 

1200 + .07d + .09b = 2600

 

.07d + .09b = 1400 (You can multiply both sides by 100 to clean up the decimal places)

 

7d + 9b = 140000 eq. 5

 

Do elimination or substitution to eq 4 and 5 and you'll get:

 

d = 11000, b = 7000