- Monthly payment = $753.45
- Interest in first month = $85
First remove the amount paid as down payment:
= 20,000 - 3,000
= $17,000
The amount to be paid monthly is a constant amount which would make it an Annuity.
The $17,000 is the present value of this Annuity so the formula for present value of annuity can be used to find the annuity.
The payment is monthly so the rate and number of periods needs to be converted:
Rate = 6%/12 = 0.5%
Period = 2 x 12 = 24 months
Annuity is:
<em>Present value of Annuity = Annuity x ( 1 - (1 + rate) ^- number of periods) / rate </em>
17,000 = A x ( 1 - ( 1 + 0.5%)⁻²⁴) / 0.5%
17,000 = A x 22.5628662
A = 17,000 / 22.5628662
A = $753.45
The interest in the first month is:
<em>= Interest rate x Amount borrowed </em>
= 0.5% x 17,000
= $85
In conclusion, the monthly payments will be $753.45 and the interest in the first month will be $85.
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