Savings and interest

Question

David deposited $4500 into two savings accounts bearing simple interest. One of the accounts has an interest rate of 3%, while the other rate is 5%. If the total interest earned after one year is $175, find the amount deposited into each of the accounts.

Answer 1

The simple interest formula is

I = PRT     interest = principal(rate)(time)

 

In this case we have P₁ at rate r= .03  and  P₂ at rate r = .05

P₁ + P₂ = 4500

 

Also we know that I₁ + I₂ = $175

where I₁ = .03(P₁) and I₂ = .05(P₂) since the time in years is T = 1

So   .03P₁ + .05P₂ = 175

 

We can do simultaneous equations

 

P₁ + P₂ = 4500

.03P₁ + .05P₂ = 175

 

Solving the top equation for P₁ we have P₁ = 4500 - P₂

Substitute that into the bottom equation and solve for P₂

 

.03(4500-P₂) + .05P₂ = 175

135 - .03P₂ + .05P₂ = 175

.02P₂ = 40

P₂ = 40/.02 = $2,000

 

Thus we have $2,000 invested at 5% interest

and $2,500 invested at 3% interest