Hi, I'm looking for someone to give a solution for these past paper questions, the topic is annuities for all the questions apart from 1a, so please provide solutions using annuities.

I have the answers, as attached, just need solutions to get to the them. Thanks in advance!

2 of 8 1. a) Define simple interest and compound interest. 5000 is invested for 5 years in two different accounts. The first account pays 2% simple interest per annum for the first two years which changes to 3% per annum for the following 3 years. The second account pays a compound interest at a rate of 2.5% per annum. Calculate the amount in each account after 5 years. Which account is more profitable? (8 marks) b) Explain what is meant by an annuity and give two examples. Let an denotes the present value of 1 paid annually in arrear at fixed rate of interest i per annum. Show that if the payment of 1 is made in advance at the same interest rate, the present value of the payment is anl vanl Explain the meaning of v and ann. Annual payments of 500 are paid into an account annually in arrear. The account earns a fixed interest of 3% per annum. What is the present value of the series of payments made over 5 years? How much extra is the present value if the payments were paid in advance over the same period of 5 years? (9 mar c) Let srl denotes an accumulation of 1 paid annually in arrear at fixed rate of interest i per annum. Show that if the investor makes equal payments of 12 at the end of each month, then the monthly payments are given by, 12) Explain the meaning of 12. You have decided to invest f1000 annually for 10 years at 3% per annum. How much should you pay monthly to accumulate the same amount after 10 years as the annual payment of 1000? 8 marks