Answer:
Present value (PV) = $57,500
Interest rate (APR) = 5.9%
Number of years = 5 years
Number of installments in a year (m) = 12
Monthly payments (A) = ?
PV = A(1 - (1 + r/m)-nm)
r/m
$57,500 = A(1 - (1 + 0.059/12)-5x12
0.059/12
$57,500 = A(1 - (1 + 0.004916666667)-60
0.004916666667
$57,500 = A(1 - (1.004916666667)-60
0.004916666667
$57,500 = A(1 - 0.745069959)
0.004916666667
$57,500 = A(51.85017778)
$57,500 = A
51.85017778
A = $1,108.96 per month
Explanation:
In this case, we need to apply the formula for present value of an ordinary annuity on the assumption that payment is made on monthly basis. The present value, interest rate (APR), number of years and number of installments in a year were provided in the question with the exception of monthly payment. Thus, the monthly payment becomes the subject of the formula.
Assuming the contract is in the form of a 60-month annuity due at an APR of 5.9 percent. Your monthly payment will be $1,103.54
Present Value Annuity due
Let C represent the monthly payment
Using this formula
Present Value Annuity due = (1 + r)PVA
Let plug in the formula
Present Value Annuity due = $57,500 = [1 +
(.059/12)] × C[{1 - 1/[1 + (.059/12)]^60} /(.059/12)
Present Value Annuity due = $57,500 = [1 +
(0.0049167)] × C[{1 - 1/[1 + (0.0049167)]^60} /(0.0049167)
$57,218.67 = $C{1 - [1/(1 + .059/12)^60]}/(.059/12)
$57,218.67 = $C{1 - [1/(1 +.0049167)^60]}/(0.0049167)
$57,218.67 = $C{1 - [1/(1.0049167)^60]}/(0.0049167)
C = $1,103.54
Inconclusion Assuming the contract is in the form of a 60-month annuity due at an APR of 5.9 percent. Your monthly payment will be $1,103.54
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