Question

A combined total of $53,000 is invested in two bonds that pay 5% and 6.5% simple interest. The annual interest is $3,085.00. How much is invested in each bond?
The amount invested at 5% is $___
The amount invested at 6.5% is $___

Answer 1

Answer:

Step-by-step explanation:

the amount of money invested at the rate of 5% is $24000

the amount of money invested at the rate of 6.5%. Is $29000

Step-by-step explanation:

Let x represent the amount of money invested at the rate of 5%.

Let y represent the amount of money invested at the rate of 6.5%.

The combined total of $53,000 is invested in two bonds that pay 5% and 6.5% simple interest.. This means that

x + y = 53000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time

Considering the investment at the rate of 5%,

P = x

R = 5

T = 1

I = (x × 5 × 1)/100 = 0.05x

Considering the investment at the rate of 6.5%,

P = y

R = 6.5

T = 1

I = (y × 6.5 × 1)/100 = 0.06.5y

The annual interest is $3,085.00.

it means that

0.05x + 0.065y = 3085 - - - - - -1

Substituting x = 53000 - y into equation 1, it becomes

0.05(53000 - y) + 0.065y = 3085

2650 - 0.05y + 0.065y = 3085

- 0.05y + 0.065y = 3085 - 2650

0.015y = 435

y = 435/ 0.015 = 29000

Substituting y = 29000 into

x = 53000 - y

x = 53000 - 29000

x = $24000