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 $2,000 per month for the next three years and then $1,000 per month for the two years after that.If the bank is charging customers 8.5 percent APR,how much would it be willing to lend the business owner?
A)$80,419.29
B)$6,494.66
C)$21,780.74
D)$96,000.00

Question

Quizplus · Accepted Answer

To find the present value of the annuities, we need to use the formula:
PV = PMT x [1 - 1/(1+r)^n]/r
where PV is the present value of the annuity, PMT is the monthly payment, r is the monthly interest rate, and n is the number of periods.

For the first set of payments:
PV1 = $2,000 x [1 - 1/(1+0.085/12)^36]/(0.085/12)
PV1 = $60,799.17

For the second set of payments:
PV2 = $1,000 x [1 - 1/(1+0.085/12)^24]/(0.085/12)
PV2 = $19,620.12

The total present value of the annuities is:
PV = PV1 + PV2
PV = $60,799.17 + $19,620.12
PV = $80,419.29

Therefore, the bank would be willing to lend the business owner up to $80,419.29. The closest answer choice to this amount is (A).

Present Value of Multiple Annuities a Small Business Owner Visits