6. If you desire to withdraw the following amounts over the next five years from a savings account that earns 8% interest compounded annually, how much do you need to deposit now? N | Amount --|------- 2 | $32,000 3 | 43,000 4 | 46,000 5 | 28,000 7. Part of the income that a machine generates is put into a sinking fund to replace the machine when it wears out. If $1,500 is deposited annually at 7% interest, how many years must the machine be kept before a new machine costing $30,000 can be purchased? 8. What is the equal payment series for 12 years that is equivalent to a payment series of $15,000 at the end of the first year, decreasing by $1,000 each year over 12 years? Interest is 8% compounded annually. 9. Find the numerical value of the following factors using (a) interpolation and (b) the formula. 1. (A/P, 13.4%, 15) 2. (P/G, 7.8%, 10) 10. Rolled ball screws are suitable for high-precision applications such as water jet cutting. Their total manufacturing cost is expected to decrease because of increased productivity, as shown in the table. Determine the equivalent annual cost at an interest rate of 8% per year. Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 -----|---|---|---|---|---|---|---|--- Cost, $1000 | 200 | 195 | 190 | 185 | 180 | 175 | 170 | 165
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To find out how much you need to deposit now, you need to calculate the present value of each withdrawal and then sum them up. The formula for present value is PV = FV / (1 + r)^n, where FV is the future value (the amount you want to withdraw), r is the interest Show more…
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3. Calculate the total number of compounding periods, n, for each of the following: a) compounded semi-annually for 7 years b) compounded monthly for 5 years c) compounded weekly for 3 years 4. Use the compound interest formula, A = P(1 + i)^n, to find the unknown value: a) A=?, P=$1300, i=0.06, n=20 b) A=$8000, P=?, i=0.05, n=24 5. Use the formula, A = P + I, to determine the amount of interest earned if the principal is $1900 and the amount is $2350. 6. How much would an investment of $800 be worth in 90 days if it earns simple interest of 8.4% per annum. 7. An investment of $2200 earned interest at 9.2% per annum compounded quarterly. How much would the investment be worth in 5 years? 8. A car loan can be taken for 4 years. At an interest rate of 8.4% per annum compounded monthly, the total cost of the car loan would be $34243.70. What is the cost of the car if you pay cash for it today rather than take out the loan? 9. Karen made an investment of $2500, two years ago to go on a trip. She invested the money at 7.2% per annum, compounded semi-annually. Her investment will mature in three years. Dwayne would also like to go on the trip. However, he hasn't started saving yet. How much must he invest today at 9.6% per annum, compounded monthly to have the same amount as Karen will have three years from now?
Umar Sohail Q.
John is 60 years old. He plans to retire in two years. He now has $\$ 400,000$ in a savings account that yields 2.9$\%$ interest compounded continuously (see Lesson 3-7). He has calculated that his final working year's salary will be $\$ 88,000 .$ He has been told by his financial advisor that he should have $60-70 \%$ of his final year's annual income available for use each year when year's annual income available for use each year when he retires. a. What is the range of income that his financial advisor thinks he must have per year once he retires? b. Use the continuous compounding formula to determine how much he will have in his account at the ages of 61 and $62 .$ c. Assume that John is planning on using 65$\%$ of his current salary in each of his first 5 years of retirement. What should that annual amount be? d. John has decided that he will need $\$ 20,000$ each year from his savings account to help him reach his desired annual income during retirement. Will John be able to make withdrawals of $\$ 20,000$ from his savings account for 20 years? Explain your reasoning.
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Retirement Income from Savings
Caroline is opening a CD to save for college. She is considering a 3 -year $\mathrm{CD}$ or a 3$\frac{1}{2}$ -year CD since she starts college around that time. She needs to be able to have the money to make tuition payments on time, and she does not want to have to withdraw money early from the CD and face a penalty. She has $\$ 19,400$ to deposit. a. How much interest would she earn at 4.2$\%$ compounded monthly for three years? Round to the nearest cent. b. How much interest would she earn at 4.2$\%$ compounded monthly for 3$\frac{1}{2}$ years? Round to the nearest cent. c. Caroline decides on a college after opening the 3$\frac{1}{2}$ -year $\mathrm{CD},$ and the college needs the first tuition payment a month before the $\mathrm{CD}$ matures. Caroline must withdraw money from the CD early, after 3 years and 5 months. She faces two penalties. First, the interest rate for the last five months of the CD was lowered to 2$\%$ . Additionally, there was a $\$ 250$ penalty. Find the interest on the last five months of the CD. Round to the nearest cent. d. Find the total interest on the 3$\frac{1}{2}$ year CD after 3 years and 5 months. e. The interest is reduced by subtracting the $\$ 250$ penalty. What does the account earn for the 3 years and 5 months? f. Find the balance on the CD after she withdraws $\$ 12,000$ after 3 years and five months. g. The final month of the CD receives 2$\%$ interest. What is the final month's interest? Round to the nearest. What is the final month's interest? Round to the nearest cent. h. What is the total interest for the 3$\frac{1}{2}$ year $\mathrm{CD} ?$ i. Would Caroline have been better off with the 3 -year CD? Explain?
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