Question

You are set to receive an annual payment of $11,300 per year for the next 19 years. Assume the interest rate is 6.2 percent. How much more are the payments worth if they are received at the beginning of the year rather than the end of the year?

Answer 1

Annual Payment = $11,300
Interest Rate = 6.20%
Period = 19 years

If payments are received at the beginning of the year:

Present Value = $11,300 + $11,300/1.062 + $11,300/1.062^2 + ... + $11,300/1.062^18
Present Value = $11,300 * 1.062 * (1 - (1/1.062)^19) / 0.062
Present Value = $131,835.29

If payments are received at the end of the year:

Present Value = $11,300/1.062 + $11,300/1.062^2 + $11,300/1.062^3 + ... + $11,300/1.062^19
Present Value = $11,300 * (1 - (1/1.062)^19) / 0.062
Present Value = $124,138.69

So, payments will worth $7,696.60 ($131,835.29 - $124,138.69)