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 $1320.

Answer 1

The principal amount deposited at 3 % is 12,000 and

The principal amount deposited at 4 $ is 2×12000 = 24,000

Explanation:

Given as :

The total interest = $ 1320

The rate of interest are 3 % and 4%

Time period = 1 year

Let the principal at 3 % =x

The principal at 4 % = twice x

I,e the principal at 4 % = 2 x

So , From simple interest method

Simple Interest =
`(\textrm Principal* rate* time)/(100)`

So,
`SI_1` =
`(\textrm x* 3* 1)/(100)`

And
`SI_2` =
`(\textrm 2 x* 4* 1)/(100)`

∵
`SI_1` +
`SI_2` = $ 1320

∴
`(\textrm x* 3* 1)/(100)` +
`(\textrm 2 x* 4* 1)/(100)` = 1320

Or, 3 x + 8 x = 1320 × 100

Or, 11 x = 132000

∴ x =
`(132000)/(11)`

I.e x = 12,000

So, The principal at 3 % is 12,000 and

The principal for 4 $ is 2×12000 = 24,000

Hence The principal amount deposited at 3 % is 12,000 and

The principal amount deposited at 4 $ is 2×12000 = 24,000 Answer