Option D
The total amount after 3 years is $ 1665.31
Solution:
Given that an investment of $1500 in an account paying 3.5% interest, compounded quarterly
To find: total amount after 3 years
The formula for total amount using compound interest is given as:
[tex]A=p\left(1+\frac{r}{n}\right)^{n t}[/tex]
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Here in this problem,
p = $ 1500
[tex]r = 3.5 \% = \frac{3.5}{100} = 0.035[/tex]
t = 3 years
n = 4 (since compounded quarterly)
Substituting the values in above formula,
[tex]\begin{aligned}&A=1500\left(1+\frac{0.035}{4}\right)^{4 \times 3}\\\\&A=1500(1+0.00875)^{12}\\\\&A=1500(1.00875)^{12}\\\\&A=1500 \times 1.110203=1665.31\end{aligned}[/tex]
Thus total amount after 3 years is $ 1665.31. Option D is correct
