It is September 1, 2010 and Richard Spender has a problem... HE SPENDS TOO MUCH! Richard has managed to rack up some impressive debts over the past few years; however, he has another problem. He has four kids: a 14 year old son, a 13 year old daughter, and twins (a boy and a girl) aged 11 who will all be going to university. Each child will begin university in September of the year they turn 18 (so for his 14 year old son, there are exactly 4 years to go, for his 13 year old daugter there are 5 years to go, and for his twins there are 7 years to go). Each child will require $5,518 per year for four years, for tuition payments payable each September. Richard would like to set up a savings plan to cover this expense. As his Financial Advisor, you can offer him an interest rate of 3% compounded monthly for a college savings plan. However, Richard must take care of his other debts as well:

Type of Debt Outstanding principal

credit card 1 $1800

credit card 2 $ 4800

credit card 3 $2100

credit card 4 $11,730

line of credit $30,000

car loan $41,000

mortgage $383,000

You have offered to consolidate all of Richard's debts into a single loan with a 10 year term and interest at 6% compounded monthly. Because he would like to continue his spending ways, Richard would like to pay as little as possible and will not accumulate any additional savings during the 10 years beyond what he is saving to meet his children's tuition expenses. Richard would like to make EQUAL payments at the end of each month that will save exactly enough to pay for his children's education and eliminate all of his debts.

a) How much must Richard save each month in the collegesavings plan?

b) How much must he pay each month towards his debts?