Question

Inga invested part of her $6000 savings in common stock and the rest in rare stamps. At the end of the year, she realized a gain of 9% on the stock and 12%on the stamps. If her savings now amounts to $6615, how much did she invest in stamps

Answer 1

The amount Inga invested in stamps is $2,500.

Step-by-step explanation:

Let x represents the amount invested in common stock. Therefore, we have:

Amount invested in common stock = x

Amount invested in stamps = 6000 - x

Rc = Rate of gain from common stock = 9%, or 0.09

Rs = Rate of gain from common stock = 12%, or 0.12

Amount of saving now = $6615

Therefore, we have

Amount of saving now = (x * (1 + Rc)) + ((6000 - x) * (1 + Rs)) ………….. (1)

Substituting all the relevant values into equation (1) and then solve for x, we have:

6615= (x * (1 + 0.09)) + ((6000 - x) * (1 + 0.12))

6615 = (x * 1.09) + ((6000 - x) * 1.12)

6615 = 1.09x + (6720 - 1.12x)

6615 = 1.09x + 6720 - 1.12x

6615 - 6720 = 1.09x - 1.12x

-105 = -0.03x

x = -105/-0.03

x = 3,500

Therefore, we have:

Amount invested in stamps = 6000 - x = $6,000 - $3,500 = $2,500

Therefore, the amount Inga invested in stamps is $2,500.