Question

General MathematicsProblem:Joe is settling his debt by paying ₱50,000 at the beginning of every 6 months for 3 years. If the loan bears an interest of 9% compounded monthly, how much is the loan?

Answer 1

Given:

Debt paying = 50,000

time = 3 year

interest rate = 9%

Joe total pay amount after 3 year is:

$\begin{gathered} =6\times50000 \\ =300000 \end{gathered}$

Formula :

$A=P(1+\frac{r}{n})^{nt}$$\begin{gathered} A=\text{ Final amount} \\ P=\text{ initial principal amount} \\ r=\text{ interest rate} \\ n=\text{ number of time} \\ t=\text{ time periods} \end{gathered}$

Given data:

$\begin{gathered} A=300000 \\ r=\frac{9}{100}=0.09 \\ n=2 \\ t=3 \end{gathered}$$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ 300000=P(1+\frac{0.09}{2})^{2\times3} \\ 300000=P(1.045)^6 \\ p=\frac{300000}{(1.045)^6} \\ p=230368.72 \end{gathered}$

So the loan amount is 230368.72