A company purchased equipment and signed a 4-year installment loan at 10% annual interest. The annual payments equal $10,600. The present value of an annuity factor for 4 years at 10% is 3.1699. The present value of a single sum factor for 4 years at 10% is .6830. The present value of the loan is:

$33,600.94

Explanation:

the present value of the loan = annuity payment x annuity factor = $10,600 x 3.1699 = $33,600.94

we can check that this amount is correct by:

first payment = $10,600 - ($33,600.94 x 10%) = $7,239.91

principal balance after first payment = $33,600.94 - $7,239.91 = $26,361.03

second payment = $10,600 - ($26,361.03 x 10%) = $7,963.90

principal balance after second payment = $26,361.03 - $7,963.90 = $18,397.13

third payment = $10,600 - ($18,397.13 x 10%) = $8,760.29

principal balance after third payment = $18,397.13 - $8,760.29 = $9,636.84

fourth payment = $10,600 - ($9,636.84 x 10%) = $9,636.32

principal balance after fourth payment = $9,636.84 - $9,636.32 = $0.52 (rounding error)

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