Question

Suzanne is looking at taking out a personal loan. Opportunity Loans is offering her $1600 at 3.45% for 1 year, with interest compounding monthly. General Loans is offering her $1600 at 4.2% for 1 year, with interest compounding quarterly. Assuming she makes no payments until the 1 year is up, how much interest will have accrued on each loan? On which loan will she earn the least amount of interest?

Answer 1

Step-by-step explanation:

So the general formula for compound interest is $A = P(1+\frac{r}{n})^{nt}$ where r is the interest rate, t is the time in years, and n is the amount of compounds per year. So plugging in the values for both equations you'll get

Opportunity Loans:

 $A = 1600(1+\frac{0.0345}{12})^{(12)(1)}$

 $A = 1600(1.002875)^{12}$

 $A \approx 1600(1.035)$

 $A = \ 1,656.08$

  Now to find the interest accrued on this loan you simply subtract 1600 from the A or final amount

 $Interest=1656.08-1600\\Interest=56.08$

General Loans:

 $A = 1600(1+\frac{0.042}{4})^{(4)(1)}$

 $A = 1600(1.0105)^4$

 $A \approx 1600(1.042)$

 $A = 1,668.27$

 To find the interest we do the same thing we did in the previous problem

 $interest = 1668.27-1600\\interest=68.27$

Opportunity loans has the least amount of interest after a year