Question

You take out a loan of $50,000 at 4% interest, compounded monthly. In two years, you pay it back. How much was the total you paid, and how much was the interest.

Answer 1

In order to calculate the total amount after 2 years, let's use the formula:

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

Where P is the principal, r is the interest rate, n is a factor that is related to the compound period and t is the time in years.

Using P = 50000, r = 0.04 and n = 12 (compounded monthly, so 12 periods of compound in a year), we have:

$\begin{gathered} A=50000(1+\frac{0.04}{12})^{12\cdot2} \\ A=50000(1+0.00333\ldots)^{24} \\ A=54.157.15 \end{gathered}$

So the total paid is $54157.15, and the interest is $4157.15.