Answer to Question #289262 in Financial Math for Chanka

Question

Assume that 4 years from now you need 1000. Your bank compounds interest at an 8% annual rate.

a. how much must you deposit now to have a balance of 1000 at year 4?

b. if you want to make equal payments at the end of years 1 through 4 to accumulate the 1000, how large must each of the 4 payments be?

c. if your father were to offer either to make payments calculated in part b above or to give you a lump sum of 750 one year from now, which option would you choose and why?

d. if you have 750 at the end of year 1, what interest rate, compounded annually, would you have to earn to have necessary 1000 at year 4?

e. suppose you can deposit only 186.29 each at the end of year 1 through 4, but you still need 1000 at the end of year 4, what interest rate, with annual compounding, is required to achieve your goal?

Answer 1

P.V =1000*pv discounting factor

=1000*1.08^-4

=1000*0.7350298

=$735.03

b. Future value (F.V)=Annuity*(1+rate)^-t

1000=annuity*[(1.08)^-4-1]/0.08

1000=x*4.506112

x=$221.92

Therefore the annuity is $221.9208

c. N=4

pmt=186.29

FV=1000

1000=186.29*[1+r)^-4-1]/r

[(1+r)^-4-1]/r=5.367974663

r=0.2

when we solve I/Y we get 0.2 = 20%

d here we can use the excel ;

PV=750

N=3

1000=750*[(1+r)^-3-1]/r

1.3333=[(1+r)^-3-1]/r

desired rate= Rate(3,-750,1000)

=0.55=55%

e. pmt=186

=rate(4,-186.29,1000)

1000=186.29*[(1+r)^-4-1]/r

=0.11

=11%