$($b$)$ A mortgage of $100,000$ is to be paid off in equal monthly instalments over $25$ years. What are the monthly mortgage payments at a constant interest rate of $6\%$ p$.$a$.?$

Answer $=644\mathrm{.}3014$

c$)$ Someone is planning to retire in $40$ years' time with a pension fund of $250,000.$ What is the required annual contribution to the pension fund if the expected rate of return on the fund is $5\%$ p$.$a$.?$

Answer $=2,069\mathrm{.}54029151$