# How to come up with a formula for amortization yearly payment but is compounded monthly?

For this problem I had a hard time answering it because I do not know how to make the payment thrice as it was also being compounded monthly:

Construct a loan amortization table for a 50,000 dollars loan at a 6% rate of interest, compounded monthly, to be repaid in 3 years with year-end payments.

All I had to do was to use the given:

$$P = 50000, i = 0.06, m = 12, n = 3$$

Using this formula to get the yearly payment:

$$A = P(i/m)/(1-(1+(i/m)^{-mn})$$

So it becomes like this:

$$A = 50000(0.06/12)/(1-(1+0.06/12)^{-12*3})$$

which equals = 1,521.10 yearly payments for 3 years. That is not true becaus if we multiply it by 3 it give us 4,563.30. Supposedly it should be greater than the principal coz the principal amount is compounded at an interest. The problem is in the formula I am using, I guess. I hope someone can spot the mistake I made. Note: can't add a tag for this question.

$$A=\frac{50000}{ \frac{1}{ \left(1+\frac{0.06}{12}\right)^{12} } + \frac{1}{\left(1+\frac{0.06}{12}\right)^{24}}+ \frac{1}{\left(1+\frac{0.06}{12}\right)^{36}} }$$
which gives $$A=$$18764\$.