If \(\$1\) was invested at \(4\%\) interest, compounded quarterly, the total value of the investment, in dollars, at the

[M7MBA]

If \(\$1\) was invested at \(4\%\) interest, compounded quarterly, the total value of the investment, in dollars, at the end of three years would be

A. \((1.4)^3\)
B. \((1.04)^{12}\)
C. \((1.04)^3\)
D. \((1.01)^{12}\)
E. \((1.01)^3\)

[spoiler]OA=D[/spoiler]

Source: Princeton Review

[deloitte247]

Given that: principal = $1, interest = 4%
Time = 3 years, n = 4 (compounded quarter)
$$A=P\cdot\left(1+\frac{r}{n}\right)^{\left(t\cdot n\right)}$$
$$A=1\cdot\left(1+\frac{4}{4}\div100\right)^{\left(3\cdot4\right)}$$
$$A=\left(1+1\cdot\frac{1}{100}\right)^{\left(12\right)}$$
$$A=\left(1+0.01\right)^{\left(12\right)}$$
$$A=\left(1.01\right)^{\left(12\right)}$$
$$Answer\ =\ D$$

[Scott@TargetTestPrep]

If \(\$1\) was invested at \(4\%\) interest, compounded quarterly, the total value of the investment, in dollars, at the end of three years would be

A. \((1.4)^3\)
B. \((1.04)^{12}\)
C. \((1.04)^3\)
D. \((1.01)^{12}\)
E. \((1.01)^3\)

[spoiler]OA=D[/spoiler]
Solution:

We can use the compound interest formula:

Future value = (present value) x (1 + rate/n)^(tn), in which rate = the annual interest rate converted to a decimal, n = the number of compounding periods per year, and t = the number of years of the investment.

Future value = 1(1 + 0.4/4)^(3 x 4) = (1.01)^12

Answer: D