Given an interest rate of 7.15 percent per year, what is the value at year t = 8 of a perpetual stream of $3,468 payments that begin at year t = 20<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To determine the value at year t = 8<\/strong> of a perpetual stream of $3,468 payments<\/strong> that begins at year t = 20<\/strong>, with an interest rate of 7.15% per year<\/strong>, we follow these steps:<\/p>\n\n\n\n The perpetuity starts at t = 20<\/strong>, so its value at t = 19<\/strong> is: PV at t = 19=Cr=3,4680.0715=48,487.41\\text{PV at t = 19} = \\frac{C}{r} = \\frac{3,468}{0.0715} = 48,487.41<\/p>\n\n\n\n We now discount the value at year 19 back to year 8: PV at t = 8=48,487.41(1+0.0715)11\u224848,487.412.1052\u224823,038.23\\text{PV at t = 8} = \\frac{48,487.41}{(1 + 0.0715)^{11}} \\approx \\frac{48,487.41}{2.1052} \\approx 23,038.23<\/p>\n\n\n\n To find the value at year 8 of a perpetuity starting at year 20, we use the time value of money<\/strong>, a core principle in finance stating that money today is worth more than the same amount in the future due to its earning potential.<\/p>\n\n\n\n A perpetuity<\/strong> is a stream of equal payments that continue forever. The present value (PV) of a perpetuity is calculated using the formula: PV=CrPV = \\frac{C}{r}<\/p>\n\n\n\n where:<\/p>\n\n\n\n Since the perpetuity begins in year 20, its present value is calculated as of year 19<\/strong>, right before the first payment. That gives us: PV19=3,4680.0715=48,487.41PV_{19} = \\frac{3,468}{0.0715} = 48,487.41<\/p>\n\n\n\n To determine the value of this perpetuity from the perspective of year 8, we need to discount<\/strong> this amount back 11 years (from t = 19 to t = 8) using the compound interest formula: PV=FV(1+r)nPV = \\frac{FV}{(1 + r)^n}<\/p>\n\n\n\n Substituting the known values: PV8=48,487.41(1.0715)11\u224848,487.412.1052=23,038.23PV_{8} = \\frac{48,487.41}{(1.0715)^{11}} \\approx \\frac{48,487.41}{2.1052} = 23,038.23<\/p>\n\n\n\n So, the value at year 8<\/strong> of the perpetual stream starting in year 20<\/strong> is $23,038.23<\/strong>. This approach correctly accounts for both the delay in cash flow and the discounting over time.<\/p>\n","protected":false},"excerpt":{"rendered":" Given an interest rate of 7.15 percent per year, what is the value at year t = 8 of a perpetual stream of $3,468 payments that begin at year t = 20 The correct answer and explanation is: To determine the value at year t = 8 of a perpetual stream of $3,468 payments that […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-19046","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=19046"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19046\/revisions"}],"predecessor-version":[{"id":19048,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19046\/revisions\/19048"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19046"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19046"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Present value of a perpetuity at year 19<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 2: Discount this amount back to year t = 8<\/strong><\/h3>\n\n\n\n
\n\n\n\n\u2705 Final Answer: $23,038.23<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words)<\/strong><\/h3>\n\n\n\n
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