Question

A total of $4000 is invested: part at 8% and the remainder at 14%. How much is invested at each rate if the annual interest is $440?

Answer 1

Answer:

$2000 is invested at 8%

$2000 is invested at 14%

Step-by-step explanation:

A total of $4000 is invested part at 8% and the remainder at 14%

Annual interest is $440.

Simple interest formula;

I = P × R × T

Where I is the interest, P is the principal, R is the rate and T is the time.

P = $4000

R = 8% and 14%

T = 1 year

I = $440

Let's say $a is invested at 8% and;

$b is invested at 14%

Then,

($a × $\frac{8}{100}$ × 1 ) + ($b × $\frac{14}{100}$ × 1) = $440

and

$a + $b = $4000

This forms a simultaneous equation;

0.08a + 0.14b = 440 ... (i)

a + b = 4000 ... (ii)

Multiplying (i) by 1 and (ii) by 0.08  we get;

0.08a + 0.14b = 440 ... (i)

0.08a + 0.08b = 320 ... (ii)

Subtracting (i) - (ii) we get;

0 + 0.06b = 120

0.06b = 120

b = 120 ÷ 0.06 = 2000

So amount invested at 14% ($b) = $2000 and,

The amount invested at 8% ($a) = $4000 - $2000 = $2000