Question

phyllis invested 66000 dollars, a portion earning simple interest rate of 5% per year and the rest earning a rate of 7% per year. after one year the total interest earned on these investments was $3980. how much money did she invest at each rate?

Answer 1

Answer:

Physliis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.

Solution:

Let Phyllis invest ‘x’ dollar at 5% per year and (66000-x) dollar at 7% per year.

We know,

$\text { Simple interest }=\frac{\text {Principal} \times r a t e \times T i m e}{100}$

In the question it is given that Simple interest earned from both the investments at the end of the year is $3980.

Using the given below equation, we will try to find out the investments at each rate.

$\begin{array}{l}{\frac{x \times 5 \times 1}{100}+\frac{(66000-x) \times 7 \times 1}{100}=3980} \\\\ {\frac{5 x}{100}+\frac{462000-7 x}{100}=3980} \\\\ {\frac{5 x+462000-7 x}{100}=3980} \\\\ {-2 \mathrm{x}+462000=3980 \times 100} \\\\ {-2 \mathrm{x}=398000-462000} \\\\ {-2 \mathrm{x}=-64000} \\\\ {\mathrm{x}=\frac{-64000}{-2}}\end{array}$

x = 32000

We can calculate amount for 7% interest rate by,

(66000-32000) =34000

Thus Phyllis invested 32000 dollar at 5% interest rate and 34000 dollar at 7% interest rate.