Question

Kevin Hall borrowed some money from his friend and promised to repay him $1,260, $1,370, $1,530, $1,650, and $1,650 over the next five years. If the friend normally discounts investment cash flows at 7.5 percent annually, how much did Kevin borrow? (Round answer to 2 decimal places, e.g. 15.25. Do not round factor values.)

Answer 1

To calculate the amount borrowed, we need to find the present values of the given cash flows. Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 7.5%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $1260/ (1 + 7.5%)+ $1370 / (1 + 7.5%)² + $1530 / (1 + 7.5%)³ + $1650 / (1 + 7.5%)⁴ + $1650 / (1 + 7.5%)⁵

PV = $1260 / (1 + 0.075)+ $1370 / (1 + 0.075)² + $1530 / (1 + 0.075)³ + $1650 / (1 + 0.075)⁴ + $1650 / (1 + 0.075)⁵

PV = $1260 / (1.075)+ $1370 / (1.075)² + $1530 / (1.075)³ + $1650 / (1.075)⁴ + $1650 / (1.075)⁵

PV = $1172.093023+ ($1370 / 1.155625) + ($1530 / 1.242296875) + ($1650 / 1.33546914063) + ($1650 / 1.43562932617)

PV = $1172.093023+ $1185.50567874 + $1231.58967134 + $1235.52087412 + $1149.3217433

PV = $5974.03

So, Kevin borrowed $5974.03