#1 Matthew makes a series of payments at the beginning of each year for 20 years. The first payment is 100. Each subsequent payment through the tenth year increases by $5 from the previous payment. After the tenth payment, each payment decreases by $2 from the previous payment. Give an actuarial expression for the present value of these payments at the time the first payment is made. No calculation needed here.
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- David would like to make a single payment of $2000 at the end of year 7 so that it will be equivalent to payments of $100, $1000, and $900 made at the ends of years 1, 12, and X years, respectively. Assuming an effective rate of interest of 5% per annum and the method of equated time, solve for X. Round your answer to 2 decimal places.Compute the present value of a perpetuity that pays $6,744 annually given a required rate of return of 9 percent per annum. Round your answer to 2 decimal places; record your answer without commas and without a dollar sign. Answer Question 4 Assume that you deposit $3,956 each year for the next 15 years into an account that pays 20 percent per annum. The first deposit will occur one year from today (that is, at t = 1) and the last deposit will occur 15 years from today (that is, at t = 15). How much money will be in the account 15 years from today? Round your answer to 2 decimal places; record your answer without commas and without a dollar sign.14. Annuity A pays X at the end of each year. The first payment occurs at time 6 years, and the last payment occurs at time 10 years. Annuity B pays $81.06 at the end of each year. The first payment occurs at time 1 year, and the last payment occurs at time 5 years. The current value of annuity B at the end of five years is $475.54. The present value at time 0 of annuity A is twice the present value at time 0 of annuity B. Determine X. D 350 E 387 A 238 C 313 B 275
- 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 $220 were made at the beginning of each quarter for 15 years at 4.6% compounded quarterly. The future value of the annuity due is $19077.23. The amount from contributions is $_______ The amount from interest is $ ________ do not round until the final answer.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) Present Value Annuity Amount i n1. ? $ 3,000 8% 52. $ 242,980 75,000 ? 43. 161,214 20,000 9 ?4. 500,000 80,518 ? 85. 250,000 ? 10 4 Sandy Kupchack just graduated from State University with a bachelor’s degree in history. During her four years at the university, Sandy accumulated $12,000 in student loans. She asks for your help in determining the…Suppose you are a beneficiary designated to immediately receive P8674 each year for 10 years, earning an annual interest rate of 6%. The future value of the stream of income payments is Round your answer to 2 decimal places. Add your answer
- A perpetuity paying $8600 at the end of each half-year is replaced with an annuity paying $X at the end of each month for 46 years. Find X if i, = 5.11 %. Answer: 151.84Find the present value (evaluated at the beginning of year 2006) of the perpetuitywhich pays $1,000 at the beginning of every year starting from year2006, but provides no payment at the beginning of every leap year. Expressyour answer in terms of the effective rate of interest i.Suppose that you deposited $5,999 at the end of each year in a Roth IRA account earning an annual rate of 5.01% for the next 15 years. How much would be on deposit at the end of the 15th year? In the space below, please indicate what the following variables are (enter answers to four decimal places and be mindful as to whether the variable is a positive or negative number): 1. PV 2. FV 3. Rate % 4. Periods 5. Payment
- a. Set up an amortization schedule for a $19,000 loan to be repaid in equal installments atthe end of each of the next 3 years. The interest rate is 8% compounded annually.b. What percentage of the payment represents interest and what percentage representsprincipal for each of the 3 years? Why do these percentages change over time?A perpetuity of $1 each year, with the first payment due immediately, has a present value of $25 at an annual effective rate of i%. The owner exchanges it for another perpetuity with the first payment due immediately and subsequent payments due at two year intervals. What should the payment of the second perpetuity be, in order to keep the same interest rate, i%, and the same present value? A B с D E Less than $1.90 At least $1.90, but less than $1.94 At least $1.94, but less than $1.98 At least $1.98, but less than $2.02 $2.02 or moreFor 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