. A debt payment of $5500 is due in 27 months. If money is worth 8.4% p.a. compounded quarterly, what is the equivalent payment

. A debt payment of $5500 is due in 27 months. If money is worth 8.4% p.a. compounded quarterly, what is the equivalent payment

 

( b) 15 months from now? 5 quarters  (c) 27 months from now? 9 quarters   (d) 36 months from now?   12 quarters

 

interest rate = 8.4/4 =2.1% = 0.021 every 3 months

 

I am assuming that the debt of $5500 is due in 27 months.  Its monetary value is not that great yet !

\(FV=PV(1+r)^n\\ PV=FV(1+r)^{-n}\\ PV=5500(1.021)^{-9}\)

 

5500*(1.021)^-9 = 4561.745063099648344

 

So if $5500 is due in 27 months its current value is  $4561.75

 

( b) 15 months from now? 5 quarters  

FV(15months)= 4561.75*1.021^5

4561.75*1.021^5 = $5061.28

 

(c) 27 months from now? 9 quarters

FV(15months)= $5500  that was given in the question

check:

FV(27months)=4561.75*1.021^9

4561.75*1.021^9 = $5500.0059523168345708    near enough :)

 

  (d) 36 months from now?   12 quarters

FV(36months)=4561.75*1.021^12

4561.75*1.021^12 = $5853.83