Question

ANSWER THE FOLLOWING:

A)A contract calls for the payment of P449,062 at the beginning of each year for the next 11 years, and P282,146 at the beginning of each year for the following 4 years. Find the present value of the payments if money is worth 7% effective.

B)A fund to replace a deteriorating machine will be formed by depositing P6,605 in the fund at the beginning of each quarter for 7 years. If the fund accumulates at 3% compounded quarterly, how much is in it at the end of 7 years?

C)A man agrees to make equal payments at the beginning of each six months for 6 years to discharge a debt of P72,608, due now. If money is worth 7% compounded semiannually, find the semi-annual payment.

D)At retirement, a man finds that his share of a pension fund is P1,512,708. What payment will this provide at the beginning of each month for 240 months, for him or his estate, if the fund is invested at 5% compounded monthly.

Answer 1

solution

A. Present value=Cashflow/(1+r)^n

where

r= discount rate

n= year of cashflow

In this case the payment is made at the beginning of each year there

Therefore in this case PV=Cashflow/(1+r)^(n-1)

Clculations given below

PV=4088908.947

Excel formula

B. Here this is a question of future value of annuity due as the payments are made at starting of quarter

FV of annuity=Annuity amount*[(((1+r)^n)-1)/r]*(1+r)

Here n= number of periods=7*4=28

r=periodic rate=3%/4=.75

FV=6605*[(((1+.0075)^28)-1)/.0075]*(1+.0075)

=206478.540 (Amount at end of 7 years)

c. Present value of annuity due= Annuity amount*[(((1-(1/(1+r)^n))/r]*(1+r)

Here r= semiannual interest rate=.07/2=.035

n= number of periods=6*2=12

Present value=72608

72608=Annuity amount*[(((1-(1/(1+.035)^12))/.035]*(1+.035)

Annuity amount i.e each semi annual payment= 7259.674

d.

Present value of annuity due= Annuity amount*[(((1-(1/(1+r)^n))/r]*(1+r)

Here r= monthly interest rate=.05/12=0.004167

n= number of periods=240

1,512,708=Annuity amount*[(((1-(1/(1+.004167)^240))/.004167]*(1+.004167)

Annuity amount=9942.109(Payment he will get every month)

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