Quarterly Payments = P = $750
Present Value of Perpetuity = PV = $13520
Let the payments start after n year = 4n quarters
Quarterly Interest Rate = i/4
=> PV = P/(1+i/4)4n + P/(1+i/4)4n+1 + .....
= 1/(1+i/4)4n-1 [ P/(1+i/4) + P/(1+i/4)2 + ...]
= 1/(1+i/4)4n-1 [ P/(i/4)]
=> (1+i/4)4n-1 = 4P/(i*PV)
=> 4n -1 = ln (4P/(i*PV)) / (1+i/4)
=> n = [1 + ln (4P/(i*PV)) / ln (1+i/4) ]/4
= [1 + ln (4*750/(i*13520)) / ln (1+i/4) ]/4
= [1 + ln (0.222/i)) / ln (1+i/4) ]/4
Hence, n = [1 + ln (0.222/i)) / ln (1+i/4) ]/4
(5) Jason purchases a deferred perpetuity for $13,520. The perpetuity has quar- terly payments of $750....
A perpetuity has annual payments. The first payment is for $330 and then payments increase by $10 each year until they become level at $600. Find the value of this perpetuity at the time of the first payment using an annual effective interest of 4%. (Round your answer to the nearest cent.)
Question 5 (6 marks) Sam pays $10,000 now to purchase a special deferred perpetuity-due. The perpetuity-due has monthly payments. Each payment is $100 for the first five years and then decreases to $50 thereafter. Given that the annual effective interest rate is 5%, calculate the deferral period.
An n year deferred perpetuity due has the following payment pattern. 300; 100; 400; 300; 100; 400; 300; 100; 400; 300; 100; 400; :::: The perpetuity has a price of 694.5262387, and this price is based on an annual effective interest rate of 10%. The payments occur on an annual basis. Find n
11. Jeff bought an increasing perpetuity-due with annual payments starting at 5 and increasing by 5 each year until the payment reaches 100. The payments remain at 100 thereafter. The annual effective interest rate is 7.5%. Determine the present value of this perpetuity. A. 700 B. 785 C. 760 D. 735 E. 810
22. An n year deferred perpetuity due has the following payment pattern 300, 100, 400, 300, 100, 400, 300, 100, 400, 300, 100, 400,.... The perpetuity has a price of 694.526 238 7. and this price is based on a annual effective interest rate of 10%. The payments occur on an annual Find n.
A perpetuity due with annual payments has the following payment pattern: 1, 2, 3, 1, 2, 3, ... Determine the present value of the perpetuity at an annual effective interest rate of 5%.
Dake is receiving a perpetuity due with annual payments. The payments are $1,000 at the beginning of each year except the payment at the beginning of every fifth year is $6,000. In other words, the first four payments at $1,000 with the fifth payment being $6,000. This is followed by four more payments of $1,000 and then a fifth payment of $6,000. This pattern continues forever. Using an annual effective interest rate of 8%. Calculate the present value of this...
an increasing perpetuity immediate makes annual payments. the first payment is 100 and each subsequent payment is larger than the preceding payment by an amount X. based on an annual effective interest rate of 10%, the present value of the perpetuity at time 0 is one half of its present value at time 20. what is rhe value of x?
A perpetuity-due with varying annual payments is available. During the first five years the payment is constant and equal to 40. Beginning in year 6, the payments start to increase. For year 6 and all future years the payment in that year is k% larger than the payment in the year immediately preceding that year. (k <6). At an annual effective interest rate of 6.7%, the perpetuity has a present value of 751.50. Calculate k.
QUESTION 6 John receives a perpetuity making payments using the following scheme: The first payment will be for 2 at the end of the 5" year The remaining payments will occur every three years, following the first payment Each subsequent payment will be X% larger than the previous payment The present value of this perpetuity at an annual effective interest rate of 10% is equal to 25. Calculate X. Give your answer rounded to two decimal places.