Question

1. Your grandfather left you an inheritance that will provide a monthly income for the next 20 years. You will receive the first payment one month from now in the amount of $2,500. Every month after that, the payment amount will increase by 0.5 percent monthly. What is your inheritance worth to you today if you can earn 7.2 percent on your investments?

Answer 1

Present value of growing annuity = P * [1 - ((1 + g) / (1 + r))ⁿ] / (r - g),

where P = first payment. This is $2,500

r = rate of return per period. This is 0.6%, or 0.006. (rate of return per month = annual rate of return / 12 = 7.2% / 12 = 0.6%)

g = growth rate. This is 0.5%, or 0.005. (monthly growth rate)

n = number of periods. This is 240. (Total number of monthly payments = number of years * 12 = 20 * 12 = 240)

Present value of growing annuity = P * [1 - ((1 + g) / (1 + r))ⁿ] / (r - g),

Present value = $2,500 * [1 - ((1 + 0.005) / (1 + 0.006))²⁴⁰] / (0.006 - 0.005)

Present value = $530,847.02