Question

You are offered a deal for purchasing a vehicle that requires you to pay $200 per month for the first year and payments of $600 per month during the second year. The APR is 18% and payments begin in one month. What is the present value of this 2-year loan?

Answer 1

Given that APR is 18%. So, Interest rate per month= 18%/12= 1.5%.

We can calculate present value of first year payments using present value of annuity formula: P*(1-(1+r)^-n)/r. On substituting, we get 200*(1-1.015^-12)/0.015= 2181.5

Next, we can calculate value of second year payments at the end of first year and then we can discount it back to present value. So, value at end of first year= 600*(1-1.015^-12)/0.015= 6544.5. Discounting it back to get the present value, 6544.5/1.015^12= 5473.74.

So, Present value of the 2-Year loan is 2181.5+5473.74= $7655.24