Question

How much would $120 invested at 6% interest compounded monthly be worth after 21 years? Round your answer to the nearest cent.A.$271.20B.$407.95C.$133.25D.$421.72

Answer 1

Explanation

To solve this problem, we will use the formula for compound interest:

$\begin{equation*} P_N=P_0\cdot(1+\frac{r}{k})^{N\cdot k}. \end{equation*}$

Where:

• Pₙ = principal amount after N years,

,

• P₀ = initial principal amount,

,

• r = interest ratio in decimals,

,

• k = compound periods per year.

From the statement, we know that:

• N = 21 years,

• P₀ = $120,

,

• r = 6% = 0.06,

,

• k = 12 (the interest is compounded monthly).

Replacing these data in the formula above, we get:

$P_{21}=\text{\ 120}\cdot(1+\frac{0.06}{12})^{21\cdot12}\cong\text{\ 421.72.}$Answer

D. $421.72