Luis will be required to make 33 payments of $206.40 each
How to determine the present value?
To calculate the monthly payment, we can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)¯ⁿ) / r]
where:
PV is the present value of the loan,
PMT is the monthly payment,
r is the monthly interest rate (15.9% APR / 12 months = 1.325% per month),
n is the total number of payments (3 years x 12 months/year = 36 months).
Since there are no payments for the first 15 months, we can calculate the present value of the loan after 15 months have passed:
PV = $4500 x (1 + 1.325%)¹⁵ = $5482.29
Now we can use the formula to solve for PMT:
$5482.29 = PMT x [(1 - (1 + 1.325%)¯³³) / 1.325%]
PMT = $206.40
Therefore, Luis will be required to make 33 payments of $206.40 each