Question

Question 24

For five years, P200,000 will be deposited in a fund at the beginning of each six months. The money’s worth is 10.5% compounded semi-annually. How much is in the fund at the end of 4 ½ years just after the last deposit is made?

P2,545,127.68

P2,745,127.68

P2,245,127.68

  P2,345,127.68

Question 25

Refer to item number 24, how much is in the fund at the end of five years?

P2,878,746.88

P2,278,746.88

P2,678,746.88

P2,478,746.88

Question 26

Refer to item number 24, what is the present value of the fund?

  P1,456,940.59

  P1,244,366.67

P1,605,870.92

  P1,849,403.39

Please answer it correctly with solutions thankss

Answer 1

24)

Amount to be invest at the BEGINNING of each year = FV of Annuity = P*[{(1+i)^n}-1]/i and FV of Single Deposit = P*[(1+i)^n]

Note: In above formula, P is the Annuity amount starting from 6 MONTHS FROM NOW. Therefore, FV of Annuity starting from TODAY will be, FV of Annuity of next 9 deposits + FV of Today’s Deposit

Where, P = 200000, i = 0.105/2 = 0.0525, n = 10-1 = 9

Therefore, FV = [200000*[{(1+0.0525)^9}-1]/0.0525] + [200000*(1+0.0525)^9]

= [200000*0.584889/0.0525] + [200000*1.584889]

= 2228148.5714 + 316.977.865

= 2545126.44 which is equivalent to 2,545,127.68

25)

Amount to be invest at the BEGINNING of each year = FV of Annuity = P*[{(1+i)^n}-1]/i and FV of Single Deposit = P*[(1+i)^n]

Note: In above formula, P is the Annuity amount starting from 6 MONTHS FROM NOW. Therefore, FV of Annuity starting from TODAY will be, FV of [FV of Annuity of next 9 deposits] after 6 months + FV of Today’s Deposit

Where, P = 200000, i = 0.105/2 = 0.0525, n = 10-1 = 9

Therefore, FV = [200000*[{(1+0.0525)^9}-1]/0.0525]*[1.0525] + [200000*(1+0.0525)^10]

= [200000*0.584889/0.0525]*[1.0525] + [200000*1.668096]

= [2228148.5714*1.0525] + 333619.203172

= 2345126.3714 + 333619.203172

= 2678745.57 which is equivalent to 2,678,746.88

26)

Amount to be invest at the BEGINNING of each year = PV of Annuity = P*[1-{(1+i)^-n}]/i

Note: For the purpose of calculation (so that formula can be applied), it will be considered that amount will be received for 9 periods at the end of each period starting from 6 months from now, and we will also add an additional annuity that will be received today. Effectively, we have a total of PV of next 9 installments and today’s installment.

Where, P = Annuity = 200000, i = Interest Rate = 0.105/2 = 0.0525, n = Number of Periods = 10-1 = 9

Therefore, Present Value = PV of next 9 Installments + Today’s Installment = [200000*{1-((1+0.0525)^-9)}/0.0525]+200000 = 1405870.919+200000 = 1,605,870.92