Present Value of Multiple Annuities A small business owner visits his bank to ask for a loan.The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for the two years after that.If the bank is charging customers 5.5 percent APR,how much would it be willing to lend the business owner?
A)$4,046.90
B)$59,293.50
C)$24.261.00
D)$66,000.00

Question

Quizplus · Accepted Answer

To calculate the loan amount, we need to find the present value of both annuities and add them together.

For the first annuity: $1,500 per month for 36 months at 5.5% APR

Using the formula for the present value of an annuity, we get:

PV = ($1,500 x ((1 - (1 + 0.055/12)^-36)/ (0.055/12)))
PV = $50,952.75

For the second annuity: $500 per month for 24 months at 5.5% APR

Using the same formula, we get:

PV = ($500 x ((1 - (1 + 0.055/12)^-24)/ (0.055/12)))
PV = $8,340.75

Adding both present values together, we get:

Loan amount = $50,952.75 + $8,340.75 = $59,293.50

Therefore, the bank would be willing to lend the business owner $59,293.50. The correct answer is (B).

Present Value of Multiple Annuities a Small Business Owner Visits