Annual Interest Rate applied to a Savings Account

Topic : Annual Interest Rate

Question : A business investes $8000 in a savings account for two years. At the begining of the second year, an additional $2500 is invested. At the end of the second year the account balance is $11445. What was the annual interest rate

Solution :
Total Investment is $8000 + $2500 = $10500
Account balance is $11445
So interewst in dollors = 11445 - 10500 = $ 945
To find interest in terms of rate 'r'
I for the first year = 8000 * (r/100) = 80r
P for second year = 8000 + 2500 + 80r = 10500 + 80r
I for second year = [10500 + 80r] * r/100 = 105r + 4/5 *r²
Hence we have 945 = 105r + 4/5 *r²
4r²+525r - 4725 = 0
r = [-525 ± √(275625+75600)] / 8
= [-525 ± √592.64] / 8
We consider the positive value
r = 8.45%
So rate of interest = 8.45%