## Related questions with answers

The following pairs of investment plans are identical except for a small difference in interest rates. Compute the balance in the accounts after $10$ and $30$ years. Discuss the difference.

Chang invests $\$ 500$ in an account that earns $3.5 \%$ compounded annually. Kio invests $\$ 500$ in a different account that earns $3.75\%$ compounded annually.

Solution

VerifiedTo get the accumulated value of an investment of $\textcolor{#c34632}{\$500}$ for two different investment plans after $\textcolor{#c34632}{10}$ and $\textcolor{#c34632}{30}$ years, we will use this formula:

$\begin{aligned} A = P \left ( 1 + \dfrac{APR}{n} \right )^{nY} \end{aligned}$

where $A$ is the accumulated balance after $Y$ years, $P$ is the starting principal, $APR$ is the annual percentage rate in decimal form, $n$ is the compounding periods per year, and $Y$ is the time in years.

In the given situation, the investment plans have the following characteristics:

**Chang's investment:**

- $APR =3.5\%$
- $n =1$ (annual compounding)

**Kio's investment:**

- $APR =3.75\%$
- $n =1$ (annual compounding)

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