Question

A new truck costs $50000. You want to pay all cash, you have $20000 in cash now and you can save $900 per month. You can earn 12% APR (monthly) on your money. How long will take you to get the money to buy the truck? I/Y? PV? FV ?PMT ?N?

Answer 1

Price = 50000

Down payment = 20000

Loan = 30000

EMI = Loan / PVAF (r%, n)
PVAF = SUm [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r)^n
r = Int rate per period
n = No. of periods

PVAF(r%, n) = 30000 / 900

= 33.3333

No. of moths at which PVAF for 1% is 33.3333 is the answer.

PVAF(1%,40) = 32.8347

PVAF(1%,41) = 33.4997

No. of Months = 40 + [ (33.333 - 32.8347 ) / ( 33.4997 - 32.8347) ]

= 40 + [ 0.4986 / 0.6650 ]

= 40 + 0.75

= 40.75 Months

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