Question

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%

Answer 1

Option D is correct.

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,

`A=P*(1+(R)/(100))^n`

here it becomes

`A=P*(1+((R)/(2))/(100))^(2n)`

`7100=6200*(1+(R)/(200))^(6)`

`(1+(R)/(200))^(6)=(7100)/(6200)`

`1+(R)/(200)=((7100)/(6200))^{(1)/(6)}`

`1+(R)/(200)=1.02284802251`

`(R)/(200)=1.02284802251-1`

`(R)/(200)=0.02284802251`

`R=0.02284802251*200`

R = 4.56960450112

R = 4.57 %

Therefore, Option D is correct.

Answer 2

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