Fund X will earn interest at an effective annual rate of 10% for the first 30 years and 6% thereafter. Fund Y will earn interest at a level effective annual rate of j. In which of the following ranges is j?
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A lump sum S deposited into either fund X or fund Y will be exactly sufficient to provide a perpetuity of $100 per year with the first payment due at the end of one year.
Fund X will earn interest at an effective annual rate of 10% for the first 30 years and 6% thereafter.
Fund Y will earn interest at a level effective annual rate of j.
In which of the following ranges is j?
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- Show Solution. Topic: Perpetuities 4. What amount is required to fund a perpetuity that begins annual payments of P50,100 immediately, if the funds can be invested to earn 11% compounded quarterly?What is the present value of a perpetuity of $8,447 per year given an interest rate of 8.2%, assuming that the first cash flow occurs today (that is, in year 0)? Record your answer as a dollar amount rounded to 2 decimal places , but do not include a dollar sign or any commas in your answer . For example , enter $ 12,327.24987 as 12327.25 .For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) Present Value Annuity Amount i = n = $3,000 75,000 20,000 80,518 1 2 3 4 5 242,980 161,214 500,000 250,000 8% 9% 10% 5 4 8 4
- Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period. $29,488 to be accumulated in 5 years; quarterly payments of $1275. %- The interest rate needed is approximately (Type an integer or decimal rounded to two decimal places as needed.)Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period. $26746 to be accumulated in 6 years; quarterly payments of $925 The interest rate needed is approximately __ % (Type an integer or decimal rounded to two decimal places as needed) Thank you so much3.) Find the present value of an annuity in perpetuity where payments are $1, 000 at the beginning of the first year, third year, etc. and payments are $1, 500 at the beginning of the second year, fourth year, etc. Here effective annual interest is 5%
- Find the periodic payments PMT necessary to accumulate the given amount in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $50,000 in a fund paying 3% per year, with quarterly payments for 20 years PMT= $ _______ ??Find the future value of each annuity due. Then determine how much of this value is from contributions and how much is from interest. Payments of $1000 made at the beginning of each semiannual period for 7 years at 8.49 % compounded semiannually The future value of the annuity due is $. (Do not round until the final answer. Then round to the nearest cent as needed.) The amount from contributions is $ The amount from interest is $ (Do not round until the final answer. Then round to the nearest cent as needed.)Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest. R=16,000; 4.3% interest compounded quarterly for 11 years. The future value of the ordinary annuity is $__ (Round to the nearest cent as needed.) The amount from contributions is $__ and the amount from interest is $__. (Round to the nearest cent as needed.)
- Find the periodic payments PMT necessary to accomulate the given account in an annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $20,000 in a fund paying 2% per year, with quarterly payments for 20 years. PMT = $a. Calculate the annual cash flows ( annuity payments) from a fixed- payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of the current year. b. Calculate the annual cash flows (annuity payments) from a fixed - payment annuity if the present value of the 20-year annuity is $1.4 million and the annuity earns a guaranteed annual return of 10 percent. The payments are to begin at the end of six years.Q. No. 02: Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. a) $300 per year for 10 years at 10% b) $100 per year for 5 years at 5% c) $300 per year for 5 years at 0% d) Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due. Q.No. 03: Solve following time line, draw a clear diagram in your answer sheet. Assume opportunity cost of 12% 6 7 3 500 500 500 300 300 300 300 300 Q. No. 04: Discuss following terms with examples; a) Perpetuity b) Par Value c) Coupon Rate d) Zero-Coupon Bond