Please explain the following problem and its concepts (with formulas).

2. Kyle received a gift of $30,000 in cash from his Grandpa on his 35-th birthday. He decided to set up an IRA and put all $30,000 in it. In addition, he would also like to make monthly deposit into this IRA, starting a month after his 35-th birthday. He wants to retire on his 65-th birthday when he'd make the last monthly deposit. Assume that the nominal annual interest is 9% (a) (10 points) If Kyle expects to have $750,000 in this IRA when he retires, what is the monthly deposit amount he must make? i = 0.75%/month, n = 360 months, A = (750000 - 30000(F/P, 0.75%, 360))(A/F, 0.75%, 360) = (750000 - 30000(14.731))(0.00055) = $169.44/month (b) (15 points) If Kyle does not put any of the $30K gift in IRA, and make monthly deposit of $160 each, but still expects $750,000 in the IRA when he retires. At about what age can he retire? A = 160, F = 750000, i = 0.75%/months F = A(F/A, 0.75%, n) (F/A, 0.75%, n) = 750000/160 = 4687.5 From Table, (F/A, 0.75%, 480) = 4681.5 n = 480 months = 40 years Kyle can retire at the age of 75 years old