please provide formulas and detailed steps

2-9. Determine the value of each described annuity. Each annuity is ordinary, unless otherwise specified. 43 (a) Invest $1000/month for 5 years, at a nominal rate of 3.2% compounding monthly. (b) An initial lump sum payment of $50,000, followed by semi-annual contributions of $10,000, growing at a nominal rate of 5.7% compounding semi-annually, for 10 years. (c) Invest $1,000 monthly into a bond fund, with a 2.4% APR, compounded monthly. Invest another $1,000 monthly into an equity fund returning 6.1% yearly, compounded monthly. Make both investments over a span of 20 years. (d) Consider the same investment scheme as (c), but add in one time initial lump sum investment of $100,000, split 20-80 into bond and equities. 2-10. You work for the shipping company Canada ex(press), and host a fleet of delivery vehicles. In 5 years the fleet will need an overhaul, which your team estimates at $1,500,000. You set up a fund which pays 3.8% compounded monthly. Determine the monthly payments into this fund to ensure you can overhaul the fleet in 5 years. 2-11. In saving for your retirement, you figure you need about $1,000,000 to maintain your lifestyle. You are currently 22, and figure you can safely put away $1000/month into an account which averages 6.6% per year (compounded monthly). At what age can you retire? 2-12. You've won a $20,000,000 lottery, and have the option of choosing an annual payment of $1,000,000 for 20 years, or a lump sum payment of $10,000,000 today. You figure you can make 7.7% in the equity market. Which option should you choose? 2-13. One retirement vehicle is to purchase an annuity through your bank, in which you deposit a certain amount of money up front, and the bank makes regular payments to you based off that deposit. Suppose you purchase such an annuity for $300,000 at a nominal rate of 6.3%. Determine the expected monthly payments, if payments are guaranteed for 10 years. Note: Often this is offered as part of life in