Question

Suppose that your roommate wants to borrow money from you. He offers three repayment plans. According to plan A, you lend him $800 now, and he repays you $1000 in two years. According to plan B, you lend him $800 now, and he repays you $500 in one year, and another $500 in two years. According to Plan C, you lend him $800 now, and he repays you $900 in one year. If you believe the interest rate is 10%, which plan do you prefer?

Answer 1

We need to use the following formula of present value here:

Present value = future value/ (1+r)ⁿ

In which, r is the rate of interest and n is the number of years.

We need to calculate the present value of the 3 plans and then select the best plan.

The present value of plan A:

$1,000/(1+0.10)² = $1,000/(1.10)² = $1,000/1.21 = $826.45

The present value of plan B:

$500(1+0.10)¹+ $500/(1+0.10)² = $500/1.1 + $500/(1.10)² = $500/1.1 + $500/1.21 = $454.54 + $413.22 = $867.76

The present value of plan C:

$900(1+0.10)¹+= $900/1.1 = $818.18

Therefore, the present valye of plan B is the highest. So, Plan B should be preferred.