Question

In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $1450.She deposited $___at 4.5% and $__at 5%

Answer 1

we will call the amount deposited at 4.5% interest x.

Since she deposits twice as much at 5% interest. That means that if the amount deposited at 4.5% is x, the amount deposited at 5% is 2x.

• The interest income due to the money deposited at 4.5% interest is:

$\text{0}.045(x)$

which is the 4.5% of the quantity x.

• The interest income due to the money deposited at 5% interes is:

$.05(2x)$

which is the 5% of the quantity 2x (the amount deposited at 5%).

Since the total annual interest income is $1450, the sum of the two previous expressions must be equal to $1450:

$0.045x+0.05(2x)=1450$

Solving the multiplication on the left side:

$0.045x+0.1x=1450$

combining the like terms on the left side:

$0.145x=1450$

Dividing each side by 0.145

$\frac{0.145x}{0.145}=\frac{1450}{0.145}$

Making the divisions

$x=10,000$

Answer:

The amount deposited at the 4.5% rate is $10,000, and

the amount deposited at 5% is twice as much: $20,000