Question

CASELEI 2 Assume that it is now January 1, 2017, and you will need P1,000 on January 1, 2020. Your Bank compounds interest at an 8 percent annual rate a. How much must you deposit on January 1, 2018 to have a balance of P1,000 on January 1, 2021? b. If you want to make equal payments on each January 1 from 2018 through 2021 to accumulate the P1,000, how large must each of the payment be? c If your father were to offer either to make the payments calculated in part b or to give vou a lump sum of P750 on January 1, 2018, which would you choose? d. If you only have P750 on January 1, 2018, what interest rate compounded annually would you have to earn to have the necessary P1,000 on January 1, 2021? e. Suppose you can deposit only P186.29 each from January 1, 2018 through January 1, 2020 but you still need P1,000 on January 1, 2021, What interest rate with annual compounding must you seek out to achieve your goal. f. To help you reach your P1,000 goal, your father offers to give you P400 on January 1, 2018. You will get a part time job and make 6 additional payments of equal amounts each 6 months thereafter. If all of this money is deposited in a bank which pays 8 percent, compounded semi-annually, how large must each of the 6 payments be? What is the effective annual rate being paid by your bank in part f? h. Reinvestment risk is the risk that maturing securities (and coupon payments for bonds) will have to be reinvested at a lower rate of interest than they were previously earning. Is there a reinvestment risk involved in the preceding analysis? If so, how might this risk be eliminated? g.

Answer 1

a.

Today's date 1-Jan-17 1-Jan-18 Deposit date Final date 1-Jan-21 Number of years 3 -final date deposit date 1000 Required amount Annual compunded rate 8% $793.66PV(8 % , 3 , 0 , - 1000) Deposit amount

b.

Number of equal payment Required amount 1000 Annual compunded rate 8% $221.92PMT(8%, 3, 0, 1000) Each payment

c.

221.92PMT(8 % , 3 , 0 , 1000 ) 944.78750 (1+8 % )^3 Each payment leading to 1000 on 1-Jan-2021 Value of 750 lump sum on 1-Jan-2021

FV of annual payment of 221.92 = 1000 (see formula in orange)

FV of 750 lump sum = 944.78

Therefore, since, 1000 > 944.78, the annual payments offered by father should be accepted.

d.

Amount in hand 750 Number of years 1000 Required amount 10%RATE ( 3, 0, -750, 1000) Required rate