SOLUTION: Brett took a loan of $55,000 and paid back a sum of $58,100 after 2 years. What is the interest he had to pay?

Question 251450: Brett took a loan of $55,000 and paid back a sum of $58,100 after 2 years. What is the interest he had to pay?
Found 2 solutions by rfadrogane, checkley77:
Answer by rfadrogane(214) (Show Source): You can put this solution on YOUR website!
The problem did not indicate whether the problem is a simple or a compound interest type.
So, were going to use this 2 method:
Let: I = the interest
P = principal amount
F = future amount
n = # of years
r = interest rate
---For simple interest rate:
I = F - P
= $58,100 - $55,000
I = $3,100
I = Prn
3,100 = 55,000(2)(r)
r = 2.82%---1st ans.
---For compound interest rate:
F = P(1+r)^n
58,100 = 55,000(1+r)^2
r = 2.8%---2nd ans.

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
55,000(1+x)^2=58,100
55,000(1+2x+x^2)=58,100
55,000+110,000x+55,000x^2=58,100
55,000x62+110,000+55,000-58,100=0
55,000x^2+110,000x-3,100=0
1,000(55x^2+110x-3.1)=0

x=(-110+-sqrt[110^2-4*55*-3.1])/2*55
x=(-110+-sqrt12,100+682])/110
x=(-110+-sqrt12,782)/110
x=(-110+-113.0575)/110
x=(-110+113.0575)/110
x=3.0575/110
x=.02779 or 2.779% is the interest rate.
Proof:
55,000(1+.02779)^2=58,100
55,000(1.02779)^2=58,100
55,000*1.05635=58,100
58,100~58,100
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