Question

How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. A(t)=P(1+r/n)^nt

Answer 1

Please enclose the "nt" inside parentheses:  A(t)=P(1+r/n)^(nt).

Then:  A = $500*(1+0.06/12)^(5*12) = $641.68

Answer 2

Answer:

$674.42.

Step-by-step explanation:

Givens

• The principal of the investment is $500.
• The interest rate compounded monthly is %6 or 0.06.
• The time invested is 5 years.

To solve these type of problems, we need to recur to Interest Compound Formula, which is

$A(t)=P(1+\frac{r}{n} )^{nt}$

Where $A$ is the total amount of money after the time compounded, $P$ is the principal, $r$ is the interest rate, $n$ is the number of compounded periods in one year and $r$ is time in years.

So,

$P=500\\r=0.06\\n=12\\t=5$

If the problem states that the interest is compounded monthly, then there are gonna be 12 compounded periods in one year. Replacing all these values, we have

$A(t)=P(1+\frac{r}{n} )^{nt}\\A(t)=500(1+\frac{0.06}{12} )^{12(5)}\\ A(t)=500(1.005)^{60}= 674.42$

Therefore, the total amount of money after 5 years is $674.42.