Fhussain74.weebly.com



Math 1324 3.1/3.2 Date: Simple Interest I = Prt where I = interest; P = principal; r = annual simple interest rate (written as a decimal) t = time in years.Future Value of simple Interest A = P + Pr t = P(1 + r t) where A = amount, or future value P = principal, or present value r = annual simple interest rate(written as a decimal) ; t = time in yearsTotal Amount Due on a Loan: a. Find the total amount due on a loan of $800 at 9% simple interest at the end of 4 months.b. Find the total amount due on a loan of $500 at 12% simple interest at the end of 30 months.(A) Your sister has loaned you $1,000 with the understanding that you will repay the principal plus 4% simple interest when you can. How much would you owe her if you repaid the loan after 1 year? After 2 years? After 5 years? After 10 years?(B) How is the interest after 10 years related to the interest after 1 year? After 2 years? After 5 years?(C) Explain why your answers are consistent with the fact that for simple interest, the graph of future value as a function of time is a straight line.Present Value of an Investment: If you want to earn an annual rate of 10% on your investments, how much (to the nearest cent) should you pay for a note that will be worth $5,000 in 9 months?Interest Rate Earned on a Note Treasury bills are one of the instruments that the U.S. Treasury Department uses to finance the public debt. If you buy a 180-day T-bill with a maturity value of $10,000 for $9,893.78, what annual simple interest rate will you earn? (Express answer as a percentage, correct to three decimal places.)Interest Rate Earned on an Investment Suppose that after buying a new car you decide to sell your old car to a friend. You accept a 270-day note for $3,500 at 10% simple interest as payment. (Both principal and interest are paid at the end of 270 days.) Sixty days later you find that you need the money and sell the note to a third party for $3,550. What annual interest rate will the third party receive for the investment? Express the answer as a percentage, correct to three decimal places.Future value of Compound Interest A = P(1 + rm)m t where A = amount (future value) at the end of n periods; P = principal (present value); r = annual nominal rate, m = number of compounding periods per year; r = rate m = number of compounding periods per yearContinuous Compound Interest Formula If a principal P is invested at an annual rate r (expressed as a decimal) compounded continuously, then the amount A in the account at the end of t years is given by A = PertComparing Interest for Various Compounding Periods If $1,000 is invested at 8% compounded(A) annually, (B) semiannually, (C) quarterly, (D) monthly, what is the amount after 5 years? Write answers to the nearest pounding Daily and Continuously What amount will an account have after 2 years if $5,000 is invested at an annual rate of 8% (A) compounded daily? (B) Compounded continuously? Compute answers to the nearest cent.What amount will an account have after 1.5 years if $8,000 is invested at an annual rate of 9% (A) Compounded weekly (1 year = 52 weeks) ? (B) Compounded continuously? Compute answers to the nearest cent.Finding Present Value How much should you invest now at 10% to have $8,000 toward the purchase of a car in 5 years if interest is compounded quarterly? (B) Compounded continuously?Computing Growth Rate $10,000 is invested in a growth-oriented mutual fund over a 10-year period would have grown to $126,000. What annual rate would produce the same growth if Interest was: (A) compounded annually? (B) Compounded continuously? Express answers as percentages, rounded to three decimal places.Math 1324 3.3/3.4 Date: Goal: Learn and apply The present values, Future Values of Annuity, Sinking Funds, Amortization.An annuity is any sequence of equal periodic payments. If payments are made at the end of each time interval, then the annuity is called an ordinary annuity. The future value, of an annuity is the sum of all payments plus all interest earned. Examples of annuities are regular deposits to a?savings account, monthly?home mortgage?payments, monthly?insurance?payments and?pension?payments.Future Value of an Ordinary Annuity FV = PMT 1+rmmt-1rm = PMT 1+in-1iAny account that is established for accumulating funds to meet future obligations or debts is called a sinking fund. If the payments are to be made in the form of an ordinary annuity, then we have formula for the sinking fund payment PMT:PMT = FV rm1+rmmt-1 = FV i1+in-1where FV = future value, PMT = periodic payment, r = rate, m = how many times compounded in a year, i = r/m = rate per period, n = mt = total number of payments. Note: Payments are made at the end of each period.What is the value of an annuity at the end of 20 years if $2,000 is deposited each year into an account earning 8.5% compounded annually? How much of this value is interest?What is the value of an annuity at the end of 10 years if $1,000 is deposited every 6 months into an account earning 8% compounded semiannually? How much of this value is interest?A company estimates that it will have to replace a piece of equipment at a cost of $800,000 in 5 years. To have this money available in 5 years, a sinking fund is established by making equal monthly payments into an account paying 6.6% compounded monthly.How much should each payment be?How much interest is earned during 5th year?A bond issue is approved for building a marina in a city. The city is required to make regular payments every 3 months into a sinking fund paying 5.4% compounded quarterly. At the end of 10 years, the bond obligation will be retired with a cost of $5,000,000.What should each payment be?How much interest is earned during the 10th year?Growth in an IRA Jane deposits $2,000 annually into a Roth IRA that earns 6.85% compounded annually. Due to a change in employment, these deposits stop after 10 years, but the account continues to earn interest until Jane retires 25 years after the last deposit was made. How much is in the account when Jane retires?Approximating an Interest Rate A person makes monthly deposits of $100 into an ordinary annuity. After 30 years, the annuity is worth $160,000. What annual rate compounded monthly has this annuity earned during this 30-year period? Express the answer as a percentage, correct to two decimal places. Amortizing a debt means that the debt is retired in a given length of time by equal periodic payments that include compound interest. The formula for Amortization is PMT =PV rm1-1+rm-mt = PV i1-1+i-nPresent Value of an Ordinary Annuity PV = PMT 1-1+rm-mtrm = PMT 1-1+i-niwhere PV = present value of all payments, PMT = periodic payment, i = rate per period, n = number of periods, Note: Payments are made at the end of each period.What is the present value of an annuity that pays $200 per month for 5 years if money is worth 6% compounded monthly?How much should you deposit in an account paying 8% compounded quarterly in order to receive quarterly payments of $1,000 for the next 4 years? Lincoln Benefit Life offered an ordinary annuity that earned 6.5% compounded annually. A person plans to make equal annualdeposits into this account for 25 years and then make 20 equal annual withdrawals of $25,000, reducing the balance in the account to zero. (a) How much must be deposited annually to accumulate sufficient funds to provide for these payments? How much total interest is earned during this entire 45-year process?If $2,000 is deposited annually for the first 25 years, how much can be withdrawn annually for the next 20 years?Assume that you buy a TV for $800 and agree to pay for it in 18 equal monthly payments at 1.5 % interest per month on the unpaid balance.(A) How much are your payments? (B) How much interest will you pay?If you sell your car to someone for $2,400 and agree to finance it at 1% per month on the unpaid balance, how much should you receive each month to amortize the loan in 24 months? How much interest will you receive?If you borrow $500 that you agree to repay in six equal monthly payments at 1% interest per month on the unpaid balance, how much of each monthly payment is used for interest and how much is used to reduce the unpaid balance? A family purchased a home 10 years ago for $80,000. The home was financed by paying 20% down and signing a 30-yearmortgage at 9% on the unpaid balance. The net market value of the house (amount received after subtracting all costs involved in selling the house) is now $120,000, and the family wishes to sell the house. How much equity (to the nearest dollar) does the family have in the house now after making 120 monthly payments? (Equity = current net market value - unpaid loan balance)You have negotiated a price of $25,200 for a new Bison pickup truck. Now you must choose between 0% financing for 48 months or a $3,000 rebate. If you choose the rebate, you can obtain a credit union loan for the balance at 4.5% compounded monthly for 48 months. (a) Which option should you choose?Which option should you choose if your credit union raises its loan rate to 7.5% compounded monthly and all other data remain the same?The annual interest rate on a credit card is 18.99%. How long will it take to pay off an unpaid balance of $847.29 if no new purchases are made and the minimum payment of $20.00 is made each month? ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download