A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $2,000 per month for the next three years and then $1,000 per month for two years after that. If the bank is charging customers 9.75 percent APR, how much would it be willing to lend the business owner

$78,443.29

Explanation:

we need to use the present value of an annuity formula:

the formula used to determine the present value factor of an annuity is:

present value annuity factor = [1 - 1/(1 + i)ⁿ ] / i

we must divide this into 2 parts:

the first part will deal with the $2,000 monthly payment

the second part deals with the $1,000 monthly payment

i = 9.75% / 12 = 0.8125%

n (first part) = 36

n (second part) = 24

the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)³⁶ ] / 0.8125% = 31.1043

the PV annuity factor for first part = [1 - 1/(1 + 0.8125%)²⁴ ] / 0.8125% = 21.7251

loan = ($2,000 x 31.1043) + ($1,000 x 21.7251)//(1 + 0.8125%)³⁶ = $62,208.60 + $16,234.69 = $78,443.29

= [1 - 1/(1 + 0.0069942)240 ] / 0.0069942 = 116.135183    

answer; ///blank(1); dealers; blank(2); brokers;