mixture problems

Question

An investment firm invested $1800 into two accounts. $1300 went to an 6% annual rate account. The rest went to a 11% annual rate account. The interest the first year amounted to:

Answer 1

We will assume yearly compounding.  That means that for an amount P at interest rate i%, P*0.01i is the amount of interest earned in a year.

 

This means that the total value of an account is

 

F = P(1+0.01i)^n

 

where 

F - value of account in n years

P - value of account at the beginning

i - yearly-compounded interest rate in percentage

n - number of years between creation of account and value in future

 

Since of the $1800, $1300 went to a 6% annual rate account, the interest from the 6% annual rate account is:

 

$1300 * 6 * 0.01 = $78

 

The rest ($1800-$1300 = $500) went to the 11% annual rate account, so the interest from the 11% annual rate account is:

 

$500 * 11 * 0.01 = $55

 

The total interest in the first year is the sum of the interests from the two accounts, so:

 

Total interest in first year = $78 + $55 = $133