hello my dear

i dont know how the answer come i have triple confuse i need how come by rules all these compound interest

FIN220 - Time value of Money Practice Questions. 1) If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years? (Answer: $16,105.10) 2) What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk. (Answer: $1,292.095014) 3) What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent. (Answer: $1,725.221703) 4) What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5. (Answer: $1,845.987222) 5) An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value? (Answer: PV=$923.975442, FV=$1,466.232904) 6) Which amount is worth more at 14 percent, compounded annually: $1,000 in hand today or $2,000 due in 6 years? (Answer: $1,000 today because PV of $2,000 is only $911.173095) 7) You need to accumulate $10,000. To do so, you plan to make deposits of $1,250 per year, with the first payment being made a year from today, in a bank account that pays 12 percent interest, compounded annually. Your last deposit will be less than $1,250 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal, and how large will the last deposit be? (Answer: 6 years, deposit in year 6 will be $1,106.013696) 8) You just started your first job, and you want to buy a house within 3 years. You are currently saving for the down payment. You plan to save $5,000 the first year. You also anticipate that the amount you save each year will rise by 10 percent a year as your salary increases over time. Interest rates are assumed to be 7 percent, and all savings occur at year end. How much money will you have for a down payment in 3 years? (Answer: $17,659.500000) 9) Today is your birthday, as for your birthday present your uncle gives you these options to choose from : a) SR50,000 in 10 years' time. If the money is placed in an investment giving 10% return, calculate the value of the investment today. b) SR18,000 today to be placed in the same investment, i.e. earning 10% return. The amount will not be withdrawn for 10 years. What will be the value of the investment at maturity? c) SR3,500 to be given annually for the next 10 years (at the end of the period) with rate of return of 8%. Compute the value of the cash flows in 10 years. FIN220 - Time value of Money Practice Questions. 10) Your client is 40 years old and wants to begin saving for retirement. You advise the client to put $5,000 a year into the stock market. You estimate that the market's return will be, on average, 12 percent a year. Assume the investment will be made at the end of the year. a. If the client follows your advice, how much money will she have by age 65? (Answer: $666,669.3503) b. How much will she have by age 70? (Answer: $1,206,663.422) 11) A 15-year security has a price of $340.4689. The security pays $50 at the end of each of the next 5 years, and then it pays a different fixed cash flow amount at the end of each of the following 10 years. Interest rates are 9 percent. What is the annual cash flow amount between Years 6 and 15? (Answer: $35.000009) 12) Find the interest rates, or rates of return, on each of the following: a) You borrow $700 and promise to pay back $749 at the end of 1 year. (Answer: 7%) b) You lend $700 and receive a promise to be paid $749 at the end of 1 year. (Answer: 7%) c) You borrow $85,000 and promise to pay back $201,229 at the end of 10 years. (Answer: 9%) d) You borrow $9,000 and promise to make payments of $2,684.80 per year for 5 years. (Answer: 15%)