Problem 1. Answer the following questions on recurrence relations. a) A person deposits $5000 in an account that yields 7% interest compounded annually. i) Set up a recurrence relation for the amount in the account at the end of n years. ao = ? an = ? ii) How much money will the account contain after 7 years? Show you calculation.
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- Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $2,500 over the next 4 years when the interest rate is 15%, how much do you need to deposit in the account? B. If you place $6,200 in a savings account, how much will you have at the end of 7 years with a 12% interest rate? C. You invest $8,000 per year for 10 years at 12% interest, how much will you have at the end of 10 years? D. You win the lottery and can either receive $750,000 as a lump sum or $50,000 per year for 20 years. Assuming you can earn 8% interest, which do you recommend and why?Use the tables in Appendix B to answer the following questions. A. If you would like to accumulate $4,200 over the next 6 years when the interest rate is 8%, how much do you need to deposit in the account? B. If you place $8,700 in a savings account, how much will you have at the end of 12 years with an interest rate of 8%? C. You invest $2,000 per year, at the end of the year, for 20 years at 10% interest. How much will you have at the end of 20 years? D. You win the lottery and can either receive $500,000 as a lump sum or $60,000 per year for 20 years. Assuming you can earn 3% interest, which do you recommend and why?You invest money into an account that earns interest at an unknown annual ratecompounded continuously. It is known that after 10 years, the amount of money inthat you have in the account doubles. Find the annual rate. Your answer is allowedto include logs if necessary.
- Suppose that you deposit $7000 in a savings account that pays 4% annual interest, with interest credited to the account at the end of each year. Assuming that no withdrawals are made, complete the following: a. Find the balance in the account after 5 years. b. Find the balance of the account after 9 years and 10 months.The balance of an interest-bearing account can be modeled by an exponential equation. For example, consider an initial deposit of $10000 at an annual interest rate of 5%. The interest earned each year is deposited into the account at the end of the year. A. Assuming that no withdrawals or deposits are made, write an equation that models the account balance after x years. Your answer B. What is the account balance at the end of the 7 years? Your answer C. Create a graph that shows the increase in the account balance over the next 15 years, including your initial deposit. Your answer D. Using the graph, estimate how many years it will take for the initial deposit to double. Your answer E. If you deposited $5000O in an account of this type, what would the account balance be when you are 50 years old assuming that you are 20 years of age right now? Your answer OCT 16Suppose you invest S11.570.00 into an account earming an interest rate of 2.484% compounded continuously for 2 yeart and thereafter earning an interest rate of 3.417% compounded weekly. How much money is in the account after 9 years? The amount in the account is (Note: Your answer should have a dollar sign and be accurate to two decimal places)
- Example 1: Finding Future Value A person deposits $5000 into an account which pays interest at a rate of 8% per year. The amount in the account after 10 years is closest to: (A) $2,792 (B) $9,000 (C) $10,795 (D) $12,165Suppose you invest $1,200 in an account paying 4% interest per year. a. What is the balance in the account after 2 years? How much of this balance corresponds to "interest on interest"? b. What is the balance in the account after 25 years? How much of this balance corresponds to "interest on interest"?Suppose you invest $103 nin a bank account, and five years later it has grown to $137.91. a. What APR did you receive, if the interest was compounded semiannually? b. What APR did you receive if the interest was compounded monthly?
- Suppose that $10,000 is deposited into a saving account that earns 6% interest, compounded annually.a) Assuming that no additional deposits or withdrawals are made, use the appropriate compound interestfactors to determine how much the account will be worth:i) After 5 years;ii) After 20 years. b) Verify that your answers in part (a) are correct by constructing a table or spreadsheet that shows howthe initial deposit will grow each year over 20 years. At a minimum, your table or spreadsheet shouldinclude a row for each year and show: the amount of money in the savings account at the start of each year. the amount of interest earned each year; and the amount of money in the savings account at the end of each year, after interest is paid.Be sure to briefly explain how your table or spreadsheet verifies your results from part (a). c) Again assuming that no additional deposits or withdrawals are made, how many years will it take untilthere is at least $50,000 in the account?Assume you deposit $5,700 at the end of each year into an account paying 11. interest. a. How much money will you have in the account in 19 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g b. How much will you have if you make deposits for 38 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g а. Future value $ 324,555.08 b. Future value $ 2,462,818.38For each of the following situations involving annulties, solve for the unknown. Assume that interest is compounded annually and that all annulty amounts are received at the end of each period. (/= Interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value 248, 196 442,750 650,000 175,000 Annuity Amount $ 5,000 80,000 60,000 155,040 8% 11% 10% n = 5 4 10 4