Mike receives $60,000$ income from developing an apartment block today. He will receive $100,000$ two years from now, and $150,000$ four years from now. How many years from now will the total investment be worth $450,000,$ assuming a constant interest rate of $5\%.$

Example $5$

Determine the present value, $P,$ and the equivalent uniform annual worth, $A,$ over the next ten years, of six payments of $1000$ made from the end of year $5$ through to the end of year ten. The interest rate is $8\%.$

Example $6$

A bank will receive annual payments of $12,000$ at the end of each of the next ten years, together with lump sums of $15,000$ and $25,000$ at the end of year $8$ and $9,$ respectively. Calculate the present worth of these payments. Interest rate is $6\%,$ The interest rate is $8\%.$