Question

A small business owner visits her bank to ask for a loan. The owner states that she can repay a loan at $2,300 per month for the next three years and then $4,600 per month for two years after that. If the bank is charging customers 8.25 percent APR, how much would it be willing to lend the business owner?

Answer 1

First calculate the value of loan at end of 3^rd year for payment of $4600, then we can use that value of loan to discount up till 3 years to get present value today:

Using financial calculator BA II Plus - Input details:	#
I/Y = Rate or yield / frequency of coupon in a year = 8.25/12 =	0.687500
PMT = Payment =	-$4,600.00
N = Total number of periods =	24
FV = Future Value =	$0.00
CPT > PV = Value of loan at end of 3rd year =	$101,452.54

Now, we can calculate the value of loan for payment stream of $2300 with loan value calculate above to get overall loan value:

Using financial calculator BA II Plus - Input details:	#
I/Y = Rate = 8.25/12 =	0.687500
PMT = Payment =	-$2,300.00
N = Total number of periods =	36
FV = Value of loan at end of 3rd year (hence, it is FV here) =	-$101,452.54
CPT > PV = Value of loan =	$152,403.92