Final answer:
To calculate the quarterly payment necessary to amortize $1000 over 14 quarters at an 8% interest rate compounded quarterly, use the present value annuity formula. The payment size is approximately $82.00 per quarter.
Step-by-step explanation:
To find the payment necessary to amortize a 8% loan of $1000 compounded quarterly, with 14 quarterly payments, we need to use the formula for the present value of an annuity:
PV = R [(1 - (1 + i)^{-n}) / i]
Where PV is the present value (or principal amount), R is the regular payment, i is the interest rate per period, and n is the number of periods. In this case:
- P = $1000 (the principal amount)
- i = 0.08 / 4 = 0.02 (the interest rate per quarter)
- n = 14 (the total number of payments)
Plugging these values into the formula and solving for R gives us:
$1000 = R [(1 - (1 + 0.02)^{-14}) / 0.02]
Calculating further we get:
R = $1000 / [(1 - (1 + 0.02)^{-14}) / 0.02]
R ≈ $82.00
Therefore, the size of each payment is approximately $82.00.