1- Jean-Rene wants to make a lump-sum deposit today such that at the end of every three months for the next five years he can receive a payment starting at $2,500 and increasing by 1% each time thereafter. At the end of the term, an additional lump-sum payment of $10,000 is required. If the annuity can earn 8.75% compounded semi-annually, what lump sum should he deposit today?

2- Sanchez is eligible to receive retirement benefits of $901.01 at age 65, but decides to start receiving them when he turns 60 instead. This incurs a 36% penalty on his benefits. By taking his retirement benefits at age 60, he will realize a monthly saving of $184.80 in retirement fund contributions. Both the benefits and contributions savings are expected to rise monthly by 0.15%. He will contribute the sum of these two amounts into his RRSP, which earns 7.35% compounded monthly until age 65, when he retires. In retirement, he will use the accumulated savings, which are expected to earn 4.5% compounded quarterly, to top up his retirement benefit payments to his pre-penalty amount. The monthly benefits are expected to rise monthly by 0.15%.

a. Calculate the total of the monthly benefits and savings at age 60.

b. Calculate the future value of the monthly savings and benefits at age 65.