Question

Phyllis invested 54000 dollars, a portion earning a simple interest rate of 4% per year and the rest earning a rate of 7% per year. After one year the total interest earned on these investments was 3270 dollar. how much money did she invest at each rate

Answer 1

$54,000

a portion at simple interest 4%

another portion simple interest 7%

earned in one year $3,270

How much on each rate ?

Simple interest formula: P * r * t where P is the principal, r is the rate, and t is the time

Earnings at 4% = P1 * 0.04 * 1 = 0.04 P1

Earnings at 7% = P2 * 0.07 * 1 = 0.07 P2

Both add 3270, so we can write:

Equation 1: 0.04 P1 + 0.07 P2 = 3270

also both quantities invested add 54000, so we can write:

Equation 2: P1 + P2 = 54000

Solving Equation 2 for P1:

P1 = 54000 - P2

Using this value into equation 1:

0.04(54000 - P2) + 0.07 P2 = 3270

Solving for P2:

2160 - 0.04 P2 + 0.07 P2 = 3270

0.03 P2 = 3270 -2160 = 1110

P2 = 1110/0.03 = 37000

P2 = 37000

Using this value into the expression we found for P1:

P1 = 54000 - P2 = 54000 - 37000 = 17000

P1 = 17000

Answer:

She invested $17,000 at 4% and $37,000 at 7%