Question

In: Finance

Today, we purchased a machine for $54,173. We paid $5,000 down and agreed to make six...

Today, we purchased a machine for $54,173. We paid $5,000 down and agreed to make six equal payments, including interest at a yearly rate of 12% compounded semiannually, every six months starting six months from now. How much should we pay every six months?

Expert Solution

Cost of machine

$54,173

Down Payment

$5,000

Pv

Balance amount tobe paid

$49,173

Annual rate of interest

12%

Rate

Semi annual interest rate

6%

Nper

Number of equal semi annual payments

6

PMT

Amount to be paid every six months starting six months from now

$9,999.95

(Using PMT function of excel with Rate=6%, Nper=6, Pv=-49173)

	This can alsobe solved using Factor Formula

	Capital Recovery Factor(CRF)=(A/P,i,N)
	(i*((1+i)^N))/(((1+i)^N)-1)
	i=interest rate=6%=0.06
	N=Number of equal payments=6
	CAF=(A/P,6%,6)
	(0.06*(1.06^6))/((1.06^6)-1)=	0.20336263
	Capital Recovery Factor(CRF)=	0.20336263
	Amount to be paid every six months starting six months from now=49173*CRF	$9,999.95

jeff jeffy answered 1 year ago

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