4. John makes deposits of 1,100 at the end of each year for n years into a fund. At time n, he uses the accumulated value of the fund to purchase an annuity Immediate that makes payments of 30,102.71 at the end of each year for 15 years. The annual effective interest rate is 13%. Calculate n. a. n = 24 نه د ل فة b. n = 26 n = 28 d. n = 20 e. n = 18
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An annuity is a payment plan that provides periodic income in return for a lump sum payment. It is widely used in insurance and retirement accounts.
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- 3. Lauren deposits: ● $240 at the beginning of year 1; $220 at the beginning of year 2; • $100 at the beginning of year 8; I into a fund. Three year after the last deposit, Lauren withdraws the accumulated value of the fund and uses it to buy a perpetuity-immediate with level payments of Z at the end of each year. All calculations assume an annual interest rate of 10%. Calculate Z. Solution:Bill makes deposits of 2,700 at the end of each year for n years into a fund. At time n, he uses the accumulated value of the fund to purchase an annuity immediate that makes payments of 197,909.20 at the end of each year for 5 years. The annual effective interest rate is 15%. Calculate n. O a. 26 O b. 29 O c. 28 O d. 24 O e. 222. Andrew deposit $2 into a fund at time 0. Money in this fund accumulates at an effective annual interest rate of i during the first 5 years, and at an effective annual interest rate of 2i thereafter. This deposit accumulates to 6.18 at the end of 10 years and to 27.47 at the end of 20 years. What is the value of the deposit at the end of 7 years? Solution:
- Ethan deposits $750 at the end of every month for 3 years and 1 months in a retirement fund at 3.86% compounded quarterly. a. What type of annuity is this? o Ordinary simple annuity o Ordinary general annuity O Simple annuity due O General annuity due b. How many payments are there in this annuity?Sean deposits $300 at the end of every month for 1 years and 6 months in a retirement fund at 4.04% compounded semi-annually. a. What type of annuity is this? O Ordinary simple annuity Ordinary general annuity O Simple annuity due O General annuity due b. How many payments are there in this annuity?how much can we paid in scolarships at the end of half year if $90.000 is deposited in a trust fund if interest is 8.5% compounded semi-anually? the amount that can be paid each half-year is $_____
- Ms Oksana Doe has just inherited an investment account worth $2,800,000 from her grandparents. The fund earns an annual interest rate of 6%. She plans to make uniform annual withdrawals from the account over the next 25 years. Answer the following two questions: 1. How much will each annual withdrawal be? OA. $223,160 OB. $47,320 OC. $50,960 OD. $232,120 OE. $218,960 2. What will be the balance in the account immediately after making the 8th annual withdrawal? OA. $1,359,698 OB. $1,048,320 OC. $2,294,110 O D. $2,431,991The sum of $159,760 is invested at 5.5% compounded monthly for four years. After the four years, the balance in the fund is converted into an ordinary annuity paying $10,240 annually. If interest on the annuity is the same, what is the term of the annuity? Select one: O a. 13.49 years b. 10.21 years С. 17.69 years d. 11.34 years e. 9.62 yearsYou deposit $9500 per quartely for 1 years at i, = 8.31 %. This fund then provides for a perpetuity of $6100 per year, with the first payment made n month after the final deposit. At the time of the first perpetuity payment, interest rates fall to i, = 2.37 %. Find n. %3D Answer: 30.36
- Every three years, D will pay Mr. J 5,000 at 8% rate to settle his loan. Mr. D will use which formula to compare with cash payment? A. Future value of IB. FV of AnnuityC. Present Value of ID.Problem: Mary deposits 1000 into a fund at the beginning of each year for 10 years. At theend of 15 years, she makes an additional deposit of X. At the end of 20 years, Maryuses the accumulated balance in the fund to buy a perpetuity-immediate with annualpayments of 2000 for 10 years, and 1000 per year thereafter. The annual effectiveinterest rate is 7%.(i) Calculate the time value of the perpetuity at the end of 20 years.(ii) Determine X.Jeff deposits 10 into a fund today and 20 fifteen years later. Interest for the firstten years is credited at a nominal discount rate of d compounded quarterly, and thereafterat a nominal interest rate of 6% compounded semiannually. The accumulated balance in thefund at the end of 30 years is 100. Calculate d.