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

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} * r a t e * 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}{(x * 5 * 1)/(100)+((66000-x) * 7 * 1)/(100)=3980} \\\\ {(5 x)/(100)+(462000-7 x)/(100)=3980} \\\\ {(5 x+462000-7 x)/(100)=3980} \\\\ {-2 \mathrm{x}+462000=3980 * 100} \\\\ {-2 \mathrm{x}=398000-462000} \\\\ {-2 \mathrm{x}=-64000} \\\\ {\mathrm{x}=(-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.