Payment of a perpetuity is done on a quarterly basis at the end of each period. The annual interest rate is 100r\% and the present value of the perpet - Mathematics MCQ Mathematics Mock Test - 10 2026 | ExamTest.live

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Payment of a perpetuity is done on a quarterly basis at the end of each period. The annual interest rate is 100 r % and the present value of the perpetuity is Rs 10,00,000. If the regular quarterly payment is Rs 40,000, what is the value of r ?

Solution & Step-by-step Explanation

Present value of a perpetuity P = \frac{R}{i}, where R is the periodic payment and i is the interest rate per period.Here P = 10, 00, 000 and R = 40, 000 (quarterly). i_{q u a r t er l y} = \frac{40 , 000}{10 , 00 , 000} = 0.04 .The annual interest rate is r = 4 \times i_{q u a r t er l y} = 4 \times 0.04 = 0.16 .Given annual rate is 100 r %, then 0.16 = 16%, so r = 0.16 .

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Payment of a perpetuity is done on a quarterly basis at the end of each period. The annual interest rate is 100 r % and the present value of the perpetuity is Rs 10,00,000. If the regular quarterly payment is Rs 40,000, what is the value of r ?

0.04

4

0.16

16

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