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- You put $250 in the bank for S years at 12%. A. If interest is added at the end of the year, how much will you have in the bank after one year? Calculate the amount you will have in the bank at the end of year two and continue to calculate all the way to the end of the fifth year. B. Use the future value of $1 table in Appendix B and verity that your answer is correct.Suppose you deposit $10 every week into an account that earns 4% interest compounded weekly. How much money (to the nearest cent) will you have in the account after 5 years? Summarize the information provided, stating the interest rate in a decimal form. d = r = N = k = Solve the problem and give your answer hereSuppose 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)
- If you deposit $P into a savings account that earns interest at a rate of i% per month for n years, the future worth in year n is represented by all of the following equations, except: (a) F = $P(F∕P, effective i/month, 12n) (b) F = $P(F∕P, effective i/quarter, 3n) (c) F = $P(F∕P, effective i/6-month, 2n) (d) F = $P(F∕P, effective i/year, n)Suppose you deposit m dollars the beginning of every month in a savings account that earns a monthly interest rate of r. For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest. Denote by An the amount of money in your account in the nth month. 1. Explain why A₁ = m dollars. 2. Explain why A₂ = m+m(1+r) dollars. 3. Write down explicit expressions for A3 and A4. This is the crucial step. 4. Explain why An = m+m(1 + r) + m(1 + r)² + ... +m(1 + r)"−¹ dollars. 5. Use the formula for a geometric sum to show that An = m (1 + r)” − 1 r dollars. 6. If your account has a monthly interest rate r = 0.002 and you deposit $200 monthly for 5 years, how much money will you have in your account after the 5 years? (Hint: How many months?)You invest B, dollars in an account that draws interest at a monthly rate of r as a decimal, compounded monthly. After t months, the balance in dollars is given by the following. B = B,(1 + r* (a) Let a denote the APR as a decimal. Then the monthly rate as a decimal is equal to a divided by 12. Express the balance in terms of the initial investment, the number of months, and the APR as a decimal. B(t) - (b) Let a denote the APR as a decimal, and let A denote the APR as a percentage. Then a is equal to A divided by 100. Express the balance in terms of the initial investment, the number of months, and the APR as a percentage. B(t) - (c) Note that y years is equivalent to 12y months. Express the balance in terms of the initial investment, the number y of years, and the APR as a percentage. B(y) =
- You open a savings account with $1,000. At the end of each year you earn 3% interest on your savings and then you deposit $1,000 into the account. Let An be the amount in the account after n years. 1. Explain why A₁ = 2,030. 2. Calculate A2 and A3. Round to the nearest penny if necessary. 3. Write a recurrence relation for An+1 in terms of An. What is the first term A₁?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 deposit $ 1296 today and your account will accumulate to $ 5637 in 9 years. What is the rate of interest? Input your answer in decimals, not percentages. Round your answer to four decimals places.
- The total amount of money in an account with P dollars invested in it is given by the formula A = P + Prt, where r is the rate expressed as a decimal and t is time (in years). If $547 is invested at 2 % , how much money will be in the account after 39 months? Round your answer to the nearest cent.In your own words, explain how compounding works. According to the rule of 72, if you deposit $100 in an account that pays 9% compound interest, how long will it take that initial deposit to reach $200? Use the matrix given below. For each type of investment, record this information: • Is the risk high, moderate, or low? • Is the return high, moderate, or low? • How does this type of investment work? Explain in one or two sentences.K You plan to deposit $700 in a bank account now and $100 at the end of the year. If the account earns 7% interest per year, what will be the balance in the account right after you make the second deposit? ... The balance in the account right after you make the second deposit will be $ (Round to the nearest dollar.)