John Wick is 50 years old and has saved nothing for retirement. However, he has just inherited £150,000 from his great grandfather and wants to invest it in a retirement plan. He plans to put the money in an investment account earning a 10% return. He will let the money accumulate for 15 years, when he will retire at the age of 65. He would like to deposit enough money so that he can begin making withdrawals of £40,000 per year starting at age 66 and continuing for 24 additional years, when he turns 90. He wants the balance in his account after the last withdrawal to be £0. After investing in his retirement plan, John wants to spend the rest of his money on a world tour.

a. How much money must John invest to achieve his goal? Construct a timeline to help visualize the details of this investment plan.

b. John realizes that once he retires he will want to invest only in less risky assets, like government securities that will earn a slightly lower rate of return—5%. So he will earn 10% until age 65, and then 5% per annum from age 65 to 90. How much money does he need to set aside now to achieve his retirement goal?

c. Suppose John has changed his mind and invests the entire inheritance into the account earning 10%. After making his last withdrawal at age 90, he wants to leave the remaining money to his niece. How much would his niece receive when John withdraws the last annual installment of £40,000?