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

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jepessoa jepessoa · Answer 1 · 2020-07-21T04:42:26+02:00

Answer:

$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

Tundexi Tundexi · Answer 2 · 2022-01-13T12:14:19+01:00

Since the bank is charging the customers 12% APR, then, the amount its would it be willing to lend her is $45,195.

Firstly, we need to calculate the present value of the annuities:

Present value = Payment * Annuity factor (PV annuity, 1%, 24 periods)

Present value = $500 * 21.243

Present value = $10,621.50

Secondly, we need to calculate the Present Value of $10,621.50:

Present Value = $10,621.50 / (1 + 12%)³

Present Value= $7560.17

Now, we will calculate the Present value of the 36 period initial $1,250 payments:

Present value = Payment * Annuity factor (PV annuity, 1%, 36 periods)

Present value = $1,250 * 30.108

Present value = $37,635

Hence, the bank will lend her $45,195 ($7,560 + $37,635).

In conclusion, since the bank is charging the customers 12% APR, then, the amount its would it be willing to lend her is $45,195.