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If $6200 is invested in a savings account for which interest is compounded semiannually, and if the $6200 turns into $7100 in 3 years, what is the interest rate of the savings account?
A.14.02% B. 3.42% C. 6.89% D.4.57%

Respuesta :

sqdancefan
The account balance A in terms of the principal P invested is
  A = P*(1 +r/n)^(nt)
  7100 = 6200*(1 +r/2)^(2*3)
  (7100/6200)^(1/6) = 1 +r/2
  2*(71/62)^(1/6) -1) = r ≈ 4.57% . . . . . . . . matches selection D

Answer:

Option D is correct.

Step-by-step explanation:

Given: P = $ 6200

           T = 3 year

            A = 7100

We have to find rate when compounded semi annually.

let say Rate be R

Formula used for Compound interest is given as,

[tex]A=P\times(1+\frac{R}{100})^n[/tex]

here it becomes

[tex]A=P\times(1+\frac{\frac{R}{2}}{100})^{2n}[/tex]

[tex]7100=6200\times(1+\frac{R}{200})^{6}[/tex]

[tex](1+\frac{R}{200})^{6}=\frac{7100}{6200}[/tex]

[tex]1+\frac{R}{200}=(\frac{7100}{6200})^{\frac{1}{6}}[/tex]

[tex]1+\frac{R}{200}=1.02284802251[/tex]

[tex]\frac{R}{200}=1.02284802251-1[/tex]

[tex]\frac{R}{200}=0.02284802251[/tex]

[tex]R=0.02284802251\times200[/tex]

R = 4.56960450112

R = 4.57 %

Therefore, Option D is correct.

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