Question

In planning her retirement Liza deposits some money at 3% interest with twice as much deposited at 4%. Find the amount deposited at each rate if the total annual interest income is $1650.

Answer 1

Answer: Liza invested $15000 at 3% and $30,000 at 4%

Explanation:

Let x be the amount invested by Liza at 3% interest then the amount she invested in 4% interest will be 2x.

We know that the compound interest with principal P is give By

`I=P(1+r)^n-P\\\Rightarrow\ I=P[(1+r)^n-1]`, where n is the number of period.

Now, interest earned in 3% (in decimal 0.03) account in 1 year is given by:-

`I_1=x[(1+0.03)^1-1]\\\Rightarrow\ I_1=x[0.03]\\\Rightarrow\ I_1=0.03x`

Similarly, interest earned in 4% (in decimal 0.03) account in 1 year is given by:-

`I_2=2x[(1+0.04)^1-1]\\\Rightarrow\ I_2=2x[0.04]\\\Rightarrow\ I_2=0.08x`

According to the question,

`I_1+I_2=1650\\\Rightarrow\ 0.03x+0.08x=1650\\\Rightarrow\ 0.11x=1650\\\Rightarrow\ x=15000`

Also, 2x=2(15000)=30000

Therefore, Liza invested $15000 at 3% and $30,000 at 4% .