A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,250 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 12 percent APR, how much would it be willing to lend the business owner

$45,195

Explanation:

we need to calculate the present value of the annuities:

first we must determine the PV (in 3 years) of the 24 $500 payments:

PV = payment x annuity factor (PV annuity, 1%, 24 periods) = $500 x 21.243 = $10,621.50

now we need to calculate the PV of $10,621.50:

PV = $10,621.50 / (1 + 12%)³ = $7560.17

finally we must calculate the PV of the 36 initial $1,250 payments:

PV = payment x annuity factor (PV annuity, 1%, 36 periods) = $1,250 x 30.108 = $37,635

The bank should lend her $7,560 + $37,635 = $45,195