Question

A money market account of $500 earns 4.5% interest compounded quarterly for 6 years. Write the equation thatrepresents this scenario

Answer 1

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

$P_N=P_0\cdot\mleft(1+\frac{r}{k}\mright)^{N\cdot k}\text{.}$

Where:

• P_N is the balance in the account after N years,

,

• P_0 is the starting balance of the account (also called an initial deposit, or principal),

,

• r is the annual interest rate in decimal form,

,

• k is the number of compounding periods in one year.

In this problem, we have that:

• N = 6 (6 years),

,

• P_N is the unknown,

,

• P_0 = 500,

,

• r = 4.5/100 = 0.045 (in decimals),

,

• k = 4 (because the interest compounded quarterly).

Replacing these values in the formula above, we find the following equation for this scenario:

$P_6=500\cdot(1+\frac{0.045}{4})^{6\cdot4}\cong653.9956$