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Oscar Montez’s savings account has a principal of $7,201. It earns 6% interest compounded quarterly. What is the amount of interest he earned by the end of the second quarter?

A. $108.01
B. $15.03
C. $231.06
D. $217.66

Respuesta :

Aliwohaish12
First find the future value
A=p (1+r/k)^kn
P 7201
R .06
K compounded quarterly 4
N 6/12 second quarter means 6 months because there are 4 quarters in a year
A=7,201×(1+0.06÷4)^(4×(6
÷12))
=7,418.65
Now find interest earned A-p
7,418.65−7,201=217.65

Answer:

D. $217.66

Step-by-step explanation:

The equation for compound interest is

[tex]A=p(1+\frac{r}{n})^{nt}[/tex], where p is the amount of principal invested, r is the interest rate, n is the number of times per year the interest is compounded and t is the number of years.

Our principal is 7201, our interest is 6% (0.06) and our value for n is 4, since it is compounded quarterly.  Our value for t will be 0.5, since 2 quarters make one half of a year:

[tex]A=7201(1+\frac{0.06}{4})^{4*0.5}\\\\=7201(1+0.015)^2\\\\=7201(1.015)^2\\\\=7201(1.030225)\\\\=7418.65[/tex]

This is the total amount in the account.  To find the amount of interest, subtract the principal:

7418.65-7201 = 217.65

This is closest to 217.66.

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