###
**CFA Practice Question**

Assume you buy a computer for $1,350 and agree to pay for it with 24 monthly payments of $45, beginning next month. What is the size of the final payment needed at month 24 to completely pay off the computer, if the interest rate you are being charged is 16% per year, compounded monthly? This final payment should exclude the final monthly payment.

A. $387.14

B. $494.39

C. $592.21

**Explanation:**This question describes a situation often called a balloon payment. On the BAII Plus, press 24 N, 16 divide 12 = I/Y, 1350 PV, 45 +/- PMT, CPT FV. On the HP12C, press 24 n, 16 ENTER 12 divide i, 1350 PV, 45 CHS PMT, FV. The answer is shown as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.

###
**User Contributed Comments**
14

User |
Comment |
---|---|

KD101 |
Payments needs to be entered negatively |

chenyx |
N=24,I/Y=16/12,PMT=-45,-->FV=1263 N=24,I/Y=16/12,PV=-1350,-->FV=1855 1855-1263=592 |

wollogo |
Thanks chenyx - that is a very good explanation, the fv of the principal minus the fv of the payments equals the principal remaining. |

julamo |
In 1 step: N=24 I/Y=1.3333 PV=-1350 PMT=45 CPT FV = 592.2 |

dimanyc |
i guess i don't understand why we compound the pmt of 45, when it clearly says that we agree to 45/month and 45*(1+r)^n per month?! |

rgat |
Not sure about this one. The question is looking for the 24th payment, which will be different from payments 1-23. Why would we not use n=23 payment periods to come up with the FV of our "obligation" @ month 23. It is that FV @ 23 which would represent the lump sum payment to net the obligation to zero. Any help... |

hannovanwyk |
No rgat. The question basically says after you make 24 payments, what amount (balance) do you need to pay to clear this debt? |

u0302638 |
I did like Julamo..although I am not very sure on using N=24.. Any advice on N=24? |

colinn |
"Exclude the final monthly payment" was confusing. $592.21 is your balance AFTER your 24th $45 payment. So in month 24 you should pay your regular $45 payment plus $592.21, total of $637.21. |

cjpatel |
you have to treat this a FV of anuuity, PMT has to be entered +ive but PV= -$1,350 |

indrayudha |
If you have doubt on N=24, look again at chenyx calculation to confirm that N=24 is valid. |

indrayudha |
"This final payment should exclude the final monthly payment." - meaning that the final payment should not factored in the 24th payment of $45. So $592.21 is correct as per chenyx and julamo's calculation. |

hyPE |
Future value of $1,350 in 24 months at a rate of 1 1/3% per month less the future value of a regular $45 saving every month at 1 1/3% per month. |

GBolt93 |
An alternative method is to calculate the PV of payments. N=24, I=16/12, FV=0, PMT=45, which get PV=919.059. Minus that from 1350=430.94, which is the PV of the obligation, then carry it forward at I=16/12 N=24 and you get 592.21 |