1 What lump sum of money must be deposited in a bank account

1. What lump sum of money must be deposited in a bank account at present time so that P700 per month can be withdrawn for seven years with the first withdrawal scheduled for 8 years frorm today?. Let-9% compounded monthly. 2.A man invests P10,000 now for the college education of his 3-year old son. If the fund ears 14% effective, how much will the son get each year starting from his 19th to 27nd birthday? 3, Compute the present value of eighteen monthly payments of $100 each, where interest is 1% per month. Payments occurs at the beginning of each months. 4. You have a building for rent and you were offered two options by a prospective client: A) P1.2M a year for 6 years, the rent being paid at the beginning of each year B) P300,000 for the 1st year, P400,000 for the 2nd year, P500,000 for the 3rd year, and P600,000 a year for the next three years. All rentals are paid at the beginning of each year. If money is worth 12%, which is the better offer? Draw the cash flow diagram for two options offered.

Solution

(1)

Monthly compounding rate = 9%/12 = 0.75%

Number of months in 7 years = 7 x 12 = 84

Number of months in 8 years = 8 x 12 = 96

After 8 years, Present Worth (PW) of future (7 years\') withdrawal = P700 x P/A(0.75%, 84) = P700 x 62.1540**

= 43,507.78

PW of this amount now (discounted by 8 years) = P43,507.78 x P/F(0.75%, 96) = P43,507.78 x 0.4881**

= P21,234.48

**P/A(r*, N) = [1 - (1 + r)^-N] / r

P/A(0.75%, 84) = [1 - (1.0075)^-84] / 0.0075 = (1 - 0.5338) / 0.0075 = 0.4662 / 0.0075 = 62.1540

**P/F(r%, N) = (1 + r)^-N

P/F(0.75%, 96) = (1.0075)^-96 = 0.4881

NOTE: As per Chegg Answering Policy, first question is answered.