Find the payment necessary to amortize a 12% loan of $900 compounded quarterly, with 16 quarterly payments.
it was wrong.
i = .12/4 =.03
n = 16
payment = p
900 = p(1 - 1.03^-16)/.03
solve for p
let me know what you get
To find the payment necessary to amortize a loan, we can use the formula for the present value of an ordinary annuity:
P = PMT * (1 - (1 + r)^(-n)) / r
Where:
P = loan amount ($900)
PMT = payment amount (unknown)
r = interest rate per period (12% per year / 4 quarters = 3% per quarter)
n = number of periods (16 quarters)
Plug in the values into the formula and solve for PMT:
P = PMT * (1 - (1 + r)^(-n)) / r
$900 = PMT * (1 - (1 + 0.03)^(-16)) / 0.03
Now, let's solve for PMT:
$900 * 0.03 = PMT * (1 - (1 + 0.03)^(-16))
27 = PMT * (1 - 0.626813467)
27 = PMT * 0.373186533
PMT = 27 / 0.373186533
PMT ≈ $72.36
Therefore, the payment necessary to amortize a 12% loan of $900, compounded quarterly with 16 quarterly payments, is approximately $72.36.
To find the payment necessary to amortize a loan, we can use the formula for the present value of an ordinary annuity.
The present value of an ordinary annuity can be calculated using the formula:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present Value (amount of the loan)
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, we are given:
Loan amount (PV) = $900
Interest rate (r) = 12% per year, compounded quarterly. Therefore, the interest rate per period will be 12% / 4 = 3%.
Number of payments (n) = 16, quarterly payments.
Let's plug in these values into the formula and solve for PMT:
PV = PMT * [(1 - (1 + r)^(-n)) / r]
Substituting the given values:
$900 = PMT * [(1 - (1 + 0.03)^(-16)) / 0.03]
Now, let's solve for PMT. First, calculate the part inside the square brackets:
(1 - (1 + 0.03)^(-16)) / 0.03 = 8.6497
Now, divide both sides by 8.6497 to solve for PMT:
$900 / 8.6497 = PMT
PMT ≈ $103.94
Therefore, the payment necessary to amortize the loan would be approximately $103.94 per quarter.