Assuming a 10 pcrcent interest rate compounded continuously, what is the present valuc of an annuity that pays $500 a year a) for the next five years, b) forever?
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- 4. At an annual effective interest rate of i, i > 0, both of the following annuities have a present value of Y: (a) a 10-year annuity-immediate with annual payments of 55. (b) a 15-year annuity-immediate with annual payments that pays 30 per year for the first 5 years, per year for the second 5 years, and 90 per year for the final 5 years. 60 Calculate Y. Solution:Choose the Best Answer. Compute the equivalent rate of 5% compounded semi-annually to a rate compounded quarterly. A . 5.96% B. 5.89% C. 4.97% D. 4.37%suppose that $2700 is set aside each year and invested in a savings account that pays 8% interest per year, componded continously, part b: in part a,suppose that an annuity will be withdrawn from savings that have been accumulated at the EOY 25. The annuity will extend from teh EOY 26 to EOY 33, what is the value of this annuity if teh interest rate and componding frquency in part a do not change
- a. What is the effective annual interest rate if the nominal annual interest rate is 10%, compounded quarterly? b. What is the effective annual interest rate if the nominal annual interest rate is 10%, compounded monthly? c. What is the effective annual interest rate if the nominal annual interest rate is 10%, compounded daily? d. What is the effective annual interest rate if the nominal annual interest rate is 10%, compounded continuously? e. At what compounding period does the effective annual interest rate very closely approximate continuous compounding? (Consider to the nearest 0.0001)2 A man borrowed Php 120,000 and promised to pay annually for 5 years. The payment starts at "X' pesos. The man intends to increase his payments by Php 5,000 at the end of each successive year. If the interest rate is 8% compounded annually, how much will the first payment cases be? If the man decides to pay annually with 8 equal payments with the first payment to be madeafter 4 years, what will be the amount of the annual payment? Construct the cash flow diagram for both cases.Suppose $5,000 is invested at an annual interest rate of 7%. Compute the balance after10 years if the interest is compounded:a. Annuallyb. Quarterlyc. Monthlyd. Continuously
- 2. My son's YouTube channel (ILYAD) is making around $1000 per year at the moment (assume payments at the end of each year). How much will he have in his RESP account 12 years from now if he keeps collecting money from YouTube? Let's assume his revenue remains the same for the next 4 years (starting today) then the revenue increases to $1500 per year, from year 4 to 8, and then it increases to $2000 per year for the remaining years. Consider 5% annual interest rate for this problem2. At what nominal rate compounded quarterly is P10,000.00 the present value of an annuity of P720.00 payable quarterly for 5 years?Show the formula and solution neatly. Due and Perpetuity What is the current value of a P 200.00 annuity be made at the beginning of each year, for 3 years if the prevailing rate of interest is 7% compounded annually?
- 8. If Ramil invested P20,000.00 at a nominal rate of interest of 14% compounded quarterly. What is the effective rate of interest?1. What is the present worth of P500 deposited at the end of every 3 months for 6 years if the interest rate is 12% compounded semi-annually? 2. Determine the present value of a perpetuity of P 100,000 payable annually, with the first payment due at the end of 10 years. Money is worth 10%. 3. How much must be deposited at 6% each year beginning on January 1, year 1 in order to accumulate P5,000 on the date of the last deposit, January 1, year 6.1. How much will be the accumulated (total) amount at the end of 9 years if a man deposits 5,000 pesos at the end of every year with an interest of 14% compounded annually. God bless!