John buys a perpetuity-due with annual payments that are adjusted each year for inflation. The first payment is 100. Inflation is 3% for the years 1-5 and 2% thereafter. Calculate the price of the perpetuity if the yield rate is an effective 6% per annum.
if i draw a time line starting at t = 0 to 5, i get
100 + 100(1.03) + ... + 100(1.03)^5
after that i get
100(1.03)^5(1.02) + 100(1.03)^5(1.02)^2 + ...
if i do geometric sum for t= 0 to 5 i get
100(1-1.03^5 / 1-1.03)
if i do geometric sum for t = 5 to infinity i get
100(1.03)^5(1.02) [ 1 + 1.02 + 1.02^2 + ...]
= 100(1.03)^5(1.02) [ 1-1.02^ infinity / 1.02] and i cannot calculate this
can someone tell me what i am doing wrong here?
if i draw a time line starting at t = 0 to 5, i get
100 + 100(1.03) + ... + 100(1.03)^5
after that i get
100(1.03)^5(1.02) + 100(1.03)^5(1.02)^2 + ...
if i do geometric sum for t= 0 to 5 i get
100(1-1.03^5 / 1-1.03)
if i do geometric sum for t = 5 to infinity i get
100(1.03)^5(1.02) [ 1 + 1.02 + 1.02^2 + ...]
= 100(1.03)^5(1.02) [ 1-1.02^ infinity / 1.02] and i cannot calculate this
can someone tell me what i am doing wrong here?
perpetuity-due question
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