Find the amount of the regular payments needed to amortize a $90000 debt at 7% compounded annually with 12 annual payments.
let the payment be P
solve for P
90000 = P( 1 - 1.07^-12)/.07
make sure you get 11331.18
To find the amount of regular payments needed to amortize a debt, you can use the formula for present value of an annuity. The formula is:
PV = PMT * \[1 - (1 + r)^(-n)\] / r
Where:
PV is the present value of the debt ($90000 in this case),
PMT is the regular payment amount we need to find,
r is the interest rate per period (7% per year in this case),
n is the total number of periods (12 annual payments in this case).
To calculate the regular payment amount (PMT), we can rewrite the formula as:
PMT = PV * r / \[1 - (1 + r)^(-n)\]
Now let's substitute the values into the formula and calculate the regular payment amount:
PV = $90000
r = 0.07 (7% expressed as a decimal)
n = 12
PMT = $90000 * 0.07 / \[1 - (1 + 0.07)^(-12)\]
PMT = $90000 * 0.07 / \[1 - (1.07)^(-12)\]
Using a calculator, compute the value inside the brackets first:
(1.07)^(-12) ≈ 0.508357
Now, substitute this value back into the formula:
PMT = $90000 * 0.07 / \[1 - 0.508357\]
PMT = $90000 * 0.07 / 0.491643
PMT ≈ $9,782.52
Therefore, the amount of the regular payments needed to amortize a $90000 debt at 7% compounded annually with 12 annual payments is approximately $9,782.52.