{"id":17910,"date":"2025-06-12T19:34:52","date_gmt":"2025-06-12T19:34:52","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=17910"},"modified":"2025-06-12T19:34:54","modified_gmt":"2025-06-12T19:34:54","slug":"which-of-the-following-statements-is-false-2","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/which-of-the-following-statements-is-false-2\/","title":{"rendered":"Which of the following statements is FALSE"},"content":{"rendered":"\n

Which of the following statements is FALSE? A) A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV). B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a stream of N equal cash flows paid at regular intervals. D) Most car loans, mortgages, and some bonds are annuities.<\/p>\n\n\n\n

The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n

The FALSE<\/strong> statement is:<\/p>\n\n\n\n

B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

Let’s analyze each statement carefully:<\/p>\n\n\n\n

A) A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV).<\/strong><\/p>\n\n\n\n

This statement is TRUE<\/strong>. A growing perpetuity is a stream of cash flows that grow at a constant rate forever. The formula for the present value (PV) of a growing perpetuity is: PV=Cr\u2212gPV = \\frac{C}{r – g}<\/p>\n\n\n\n

where<\/p>\n\n\n\n

    \n
  • CC = cash flow at the end of the first period,<\/li>\n\n\n\n
  • rr = discount rate,<\/li>\n\n\n\n
  • gg = growth rate.<\/li>\n<\/ul>\n\n\n\n

    For this formula to be valid, the discount rate rr must be greater<\/strong> than the growth rate gg. If g\u2265rg \\geq r, the denominator becomes zero or negative, causing the PV to approach infinity or be undefined. Thus, if growth exceeds the discount rate, the present value grows without bound, becoming infinitely large.<\/p>\n\n\n\n

    \n\n\n\n

    B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.<\/strong><\/p>\n\n\n\n

    This statement is FALSE<\/strong>. In fact, it’s the opposite:<\/p>\n\n\n\n

      \n
    • An annuity<\/strong> is a series of fixed cash flows paid for a finite number of periods<\/strong>.<\/li>\n\n\n\n
    • A perpetuity<\/strong> is a series of fixed cash flows paid forever<\/strong>, with no end<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      So, perpetuities do not<\/strong> end after some fixed number of payments\u2014they continue indefinitely. The key difference is the length of the payment stream: finite for annuities, infinite for perpetuities.<\/p>\n\n\n\n

      \n\n\n\n

      C) An annuity is a stream of N equal cash flows paid at regular intervals.<\/strong><\/p>\n\n\n\n

      This statement is TRUE<\/strong>. By definition, an annuity consists of equal payments spaced evenly over time, usually monthly, annually, etc., and these payments occur for a set number NN of periods.<\/p>\n\n\n\n

      \n\n\n\n

      D) Most car loans, mortgages, and some bonds are annuities.<\/strong><\/p>\n\n\n\n

      This statement is TRUE<\/strong>. Loans like car loans and mortgages involve fixed payments over a certain period, making them annuities. Some bonds also pay fixed coupon payments for a defined period, which classifies them as annuities.<\/p>\n\n\n\n

      \n\n\n\n

      Summary:<\/h3>\n\n\n\n
        \n
      • Statement B incorrectly defines a perpetuity.<\/li>\n\n\n\n
      • The key conceptual difference is the duration<\/strong> of payments\u2014annuities end; perpetuities do not.<\/li>\n\n\n\n
      • Statements A, C, and D are accurate.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

        Which of the following statements is FALSE? A) A growing perpetuity, where the rate of growth is greater than the discount rate, will have an infinitely large present value (PV). B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments. C) An annuity is a […]<\/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-17910","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17910","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=17910"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17910\/revisions"}],"predecessor-version":[{"id":17911,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17910\/revisions\/17911"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}