4. It is desired to invest a lump sum of money on a boy's 4th birthday to provide him $2,000 on each birthday from the 18th to the 22nd, both inclusive. lf the interest of 12% can be obtained from the investment, what lump sum must be invested? 5. Assume that in the circumstances described in Problem 4, it is not practicable to invest the entire lump sum indicated by your calculations. $500 will be invested on the 4th birthday and a uniform annual deposit in the fund will be made on the 5th and 12th birthdays, both inclusive. Assuming 12% interest, what must be the annual deposit from the 5th to 12th birthdays? 6. Solve the following, using interest at 12% compounded annually: (a) What is the amount that will be accumulated in a fund at the end of 15 years if $200 is deposited in the fund at the beginning of each of the 15 years? (b) Uniform deposits are to be made on 1 of 2012, 2013, 2014 and 2015 into a fund that is intended to provide $1,000 on January 1 of 2025 2026, and 2027. What must be the size of these deposits