Paula split an inheritance between two investments, one a certificate of deposit paying 7% annual interest, and the other a promising biotech company offering an annual return of 10%. She invested twice as much in the 10% investment as she did in the 7% investment. If her combined annual income from the two investments was $2,700, how much did she inherit?
A) $22000
B) $32000
C) $20000
D) $30000
E) $31000

Question

Quizplus · Accepted Answer

Let's say Paula inherited $x.

Then, the amount Paula invested in the certificate of deposit paying 7% interest = $\frac{x}{3}$

And the amount Paula invested in the promising biotech company offering an annual return of 10% = $\frac{2x}{3}$

Annual income from the first investment = 0.07 * $\frac{x}{3}$ =  $\frac{0.07x}{3}$
Annual income from the second investment = 0.1 * $\frac{2x}{3}$ = $\frac{0.2x}{3}$

Total annual income = $\frac{0.07x}{3}$ + $\frac{0.2x}{3}$ = $\frac{0.27x}{3}$ = $\frac{0.09x}{1}$ (since $\frac{1}{3}$ + $\frac{2}{3}$ = $\frac{3}{3}$)

It is given that the total annual income from the two investments was $2,700.

Therefore, $\frac{0.09x}{1}$ = $2,700$
Or, $x$ = $\frac{2,700}{0.09}$ = $30,000$

Hence, Paula inherited $30,000. The answer is option D.

Paula Split an Inheritance Between Two Investments, One a Certificate