Question

A debt of $18 000 is being repaid by 15 equal semi annual payments with the first payment to be made six months from now. Interest is at the rate of 7% compounded semiannually. However after 2 years, the interest rate increases to 8% compounded semiannually.If the debt must be paid off on the original date agreed upon, find the new annual payment.

Answer 1

How far have you gotten?

P = Original Payment
i = 0.07 -- Annual Percentage Rate to be compounded semi-annually.
j = 0.07/2 -- Semi-annual percentage rate.
v = 1/(1+j) -- Semi-annual discount factor.

\(18000 = P(v + v^{2} + ... + v^{15}) = P\cdot\dfrac{v-v^{16}}{1-v} = P\cdot\dfrac{v(1-v^{15})}{j\cdot v} = P\dfrac{1-v^{15}}{j}\)

Thus, \(P = \dfrac{18000\cdot j}{1-v^{15}}\)

Any of that look familiar?