Annuity payment formula

Question

Here is the problem. I want to take loan of $24{,}000$\$, and I want to repay it in series of equal payments monthly in time of five year. I use this formula to get the monthly annuity $$ \operatorname{P}= \frac{r\operatorname{PV}}{1-(1+r)^{-n}}$$ Where $\operatorname{P}$ is the payement, $\operatorname{PV}$ the present value, $r$ the rate per period and $n$ the number of periods.

But I get amount of monthly annuity $2169$\$, whic is wrong, the correct annuity is $489$\$.

Accrued interest is $8.99$.

Can anyone check this?

Answer 1

$$ \operatorname{P}= \frac{r\operatorname{PV}}{1-(1+r)^{-n}}$$

$$ \operatorname{P} = \frac{(8.99\%/12) \cdot 24000}{1-(1+(8.99\%/12))^{-60}}$$

$$ \operatorname{P} = \$498$$

$(8.99\%/12 \approx 0.00749)$

Answer 2

$24,000, 60 months at 8.99%. Here are my calcs.

$B =$ monthly payment $\sum_1^{60} \frac{1}{(1+r/12)^i}$

$B =$ monthly payment $\dfrac{1-(1+r/12)^{-60}}{r/12}$ monthly payment = $B \dfrac{r/12}{1-(1+r/12)^{-60}}$

monthly payment = $\dfrac{24,000 * (0.0899/12)}{1-(1.0899)^{-60}}$ = $\dfrac{24,000 * (0.00742)}{0.361} = 498$