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

Answer:

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

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

Step-by-step 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 = $\dfrac{\textrm Principal\times rate\times time}{100}$

So, $SI_1$ =  $\dfrac{\textrm x\times 3\times 1}{100}$

And $SI_2$ =  $\dfrac{\textrm 2 x\times 4\times 1}{100}$

∵  $SI_1$ +  $SI_2$ = $ 1320

∴  $\dfrac{\textrm x\times 3\times 1}{100}$ + $\dfrac{\textrm 2 x\times 4\times 1}{100}$ = 1320

Or, 3 x + 8 x = 1320 × 100

Or, 11 x = 132000

∴   x = $\frac{132000}{11}$

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