Answer:
C. $1030.34
Explanation:
Given:
Principal = $1,000
Interest = 3%
Number of Times = Quarterly
Time = 1 year
Interest Type = Compound Interest
Required
Amount at the end of the year
To solve this, I'll make use of Amount formula which is;
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Using compound interest notations, the given parameters are:
P = $1,000
r = 3%
t = 1
Quarterly means 4 times a year;
So, n = 4
Solving for Amount (A), the formula becomes
[tex]A = \$ 1000(1 + \frac{3\%}{4})^{4 * 1}[/tex]
[tex]A = \$ 1000(1 + \frac{3\%}{4})^{4}[/tex]
Convert percent to decimal
[tex]A = \$ 1000(1 + \frac{0.03}{4})^{4}[/tex]
[tex]A = \$ 1000(1 + 0.0075)^{4}[/tex]
Solve the expression in the bracket
[tex]A = \$ 1000(1 .0075)^{4}[/tex]
Solve the exponent
[tex]A = \$ 1000 * 1.03033919066[/tex]
[tex]A = \$ 1030.33919066[/tex]
[tex]A = \$ 1030.34[/tex] (Approximated)
Hence, the amount at the end of the year is approximately $1030.34
