Question

Blake has a total of

$13,000

to invest in two accounts. One account earns

2

%

simple interest, and the other earns

5

%

simple interest. How much should be invested in each account to earn exactly

$380

at the end of

1

yr

?

Answer 1

Let the amount invested in account 1 be x and that in account 2 be y.

Then, as he invests a total of $13000 in two accounts together,

x + y = 13000 → (1)

Account 1 earns 2% simple interest.

So after a year the interest earned from account 1 = 2%x = 0.02x

Account 2 earns 5% simple interest.

So after a year the interest earned from account 2 = 5%y = 0.05y

Also total interest to be earned after a year is $380.

0.02x + 0.05y = 380

On multiplying by 100,

2x + 5y = 38000 → (2)

Multiply equation (1) by -2 and add to (2)

2x + 5y = 38000

-2x - 2y = -26000

3y = 12000

y = 12000/3 = 4000

x = 13000 - 4000 = 9000

Amount invested in account 1 = $9000

Amount invested in account 2 = $4000