Respuesta :
Answer:
Compound interest is better, by $14.36.
Step-by-step explanation:
Simple Interest:
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Total amount in compound interest:
$3,000 in a certificate of deposit that pays 2.8% interest, compounded annually for 4 years. This means, respectively, that [tex]P = 3000, r = 0.028, n = 1, t = 4[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(4) = 3000(1 + \frac{0.028}{1})^{4} = 3350.38[/tex]
Total amount in simple interest:
[tex]P = 3000, I = 0.028, t = 4[/tex]
So
[tex]E = P*I*t = 3000*0.028*4 = 336[/tex]
[tex]T = E + P = 3000 + 336 = 3336[/tex]
Which is better and by how much?
Higher earning with compound interest, so it is better.
3350.36 - 3336 = 14.36
Compound interest is better, by $14.36.
