Answer:
[tex] PMT = \frac{45300}{[\frac{1- \frac{1}{(1+0.0425/12)^{12*10}}}{0.0425/12}]}= \frac{45300}{97.62046852}= 464.042[/tex]
Explanation:
For this case we can use present value calculation for an ordinary annuity in order to calculate the PMT each month.
The formula is given by:
[tex] PV = PMT [\frac{1- \frac{1}{(1+i/n)^{nt}}}{i/n}][/tex] (1)
Where:
PMT represent the monthly payment
PV represent the present value on this case 45300
i represent the discount rate and for this case we know that i =4.25 % = 0.0425
n represent the number of periods that the interest is compound in 1 year, we can assume that n =12 for this case
t represent the number of periods for which the annuity will last t= 10 years
If we solve for the PV from formula (1) we got:
[tex] PMT = \frac{PV}{[\frac{1- \frac{1}{(1+i/n)^{nt}}}{i/n}]}[/tex] (2)
And replacing the values we got:
[tex] PMT = \frac{45300}{[\frac{1- \frac{1}{(1+0.0425/12)^{12*10}}}{0.0425/12}]}= \frac{45300}{97.62046852}= 464.042[/tex]
And that would be the final answer for this case 464.042
Hi there
The formula of the present value of annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value 45300
PMT monthly payment?
R interest rate 0.0425
K compounded monthly 12
N time 10 years
We need to solve for pmt
Pmt=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=45,300÷((1−(1+0.0425÷12)^(
−12×10))÷(0.0425÷12))
=464.04...answer
