Compound Interest and Rate Essay - 1836 Words

Solution to Problem Set 1 1. You are considering various retirement plans. Your goal is to have a lump sum of $3,000,000 available (‘in the bank’) when you retire at age 67. The various plans, with their payment schedules, are listed below. In each case, calculate the payment(s) that must be made into the plan to ensure that you have the $3,000,000 available. For each plan, you may assume that your opportunity cost of funds is 6% per year; for each plan, you may assume that the phrase â€Å"at age XX† means the same thing as â€Å"on your XX’th birthday†. Plan 1: Single lump sum at age 25 Plan 2: Single lump sum at age 50 Plan 3: Equal annual payments, commencing at age 31 and ending at age 67 Plan 4: Equal annual†¦show more content†¦Note that the monthly inflation rate is 2.4%/12, or 0.2% per month. We need to compound the first tuition cash flow, which occurs in 16 years, by 16 X 12 = 192 months, the second tuition cash flow by 17 X 12 = 204 months, etc. First tuition cash flow = 38,500 * (1.002)192 = 56,501.93 Second tuition cash flow = 38,500 * (1.002)204 = 57,872.99 Third tuition cash flow = 38,500 * (1.002)216 = 59,277.32 Fourth tuition cash flow = 38,500 * (1.002)228 = 60,715.73 If we wish to discount these annual cash flows, we need an effective annual rate. Currently, the interest rate is given to us as 6.0% per year, compounded monthly. This implies an effective monthly rate of 0.50%, or an effective annual rate of: (1.0050)12 – 1 = 6.1678% The value at t=16 of these cash flows, with r=6.1678%: V =56,501.93 + 57,872.99/(1.061678) + 59,277.32/(1.061678)2+ 60,715.73/(1.061678)3 V = $214,339.59 f) Calculate the value, at t=16, of four years’ worth of college tuition if tuition grows at the recent education inflation rate of 6.4% per year, compounded monthly. Changing the inflation rate in the problem above to 6.4% per year, compounded monthly (or 0.533% per month), we have tuition cash flows of t Cash flow 16 106,904.64 17 113,950.85 18 121,461.47 19 129,467.13 And the value at t=16, with our opportunity cost ofShow MoreRelatedMathematics of Finance Hw Essay735 Words   |  3 Pagesannual simple interest rate of 6%, for 10 months b) To invest 5,000â‚ ¬ in a bank account that offers an annual compound interest rate of 6%, for 10 months The bank pays interests once per month a) b) So, option b) is the best. 2- Prove which of the following options is the most interesting one: a) To invest 5,000â‚ ¬ in a bank account that offers an annual simple interest rate of 6%, for 1 year b) To invest 5,000â‚ ¬ in a bank account that offers an annual compound interest rate of 6%, for 1Read MoreCompound Interest Formul The Magic Formula For Becoming Rich And Building Wealth980 Words   |  4 PagesCompound Interest Formula - The Magic Formula for Becoming Rich and Building Wealth By Keelan Cunningham | Submitted On February 14, 2011 Recommend Article Article Comments Print Article Share this article on Facebook Share this article on Twitter Share this article on Google+ Share this article on Linkedin Share this article on StumbleUpon Share this article on Delicious Share this article on Digg Share this article on Reddit Share this article on Pinterest Expert Author Keelan CunninghamRead Morefinance lab week 3787 Words   |  4 PagesFIN 370 Lab Study Guide - All Weeks - Additional Formula (Compound interest) to what amount will the following investments accumulate? a. $5,000 invested for 10 years at 10 percent compounded annually 5000 x (1.10)^10 = 5000 x2.5937 =12968.5 b. $8,000 invested for 7 years at 8 percent compounded annually 8000 x (1.08)^7 = 8000 x 1.7138 = 13710.59 c. $775 invested for 12 years at 12 percent compounded annually 775 x (1.12)^12 = 775 x3.8959 =3019.38 d. $21,000 invested for 5 years at 5 percentRead MoreAnnuity1659 Words   |  7 Pagescomputed the future value of an investment when a fixed amount of money is deposited in an account that pays interest compounded periodically. Often, however, people do not deposit money and then sit back and watch it grow. Rather, money is invested in small amounts at periodic intervals. Consider these problems: 1. Chrissy deposits $200 each year into a savings account that has an annual interest rate of 8% compounded annually. How much money will Chrissy have in her account after three years? Hint: MakeRead MoreBusiness Math1006 Words   |  5 PagesSimple interest is the interest that is computed on the original principal only. If I denotes the interest on a principal P (in dollars) at an interest rate of r per year for t years, then we have I = Prt The accumulated amount A, the sum of the principal and interest after t years is given by and is a linear function of t. A= P + I = P + Prt = P(1 + rt) A bank pays simple interest at the rate of 8% per year for certain deposits. a. If a customer deposits $1000 and makes no withdrawalsRead MoreLala975 Words   |  4 Pages*Find the compound amount for each deposit and the amount of interest earned Ex22 15ooo$ at 6% compounded monthly for 10 years The principle is P=$15000 The interest rate per month is i=r/12=0.06/12 The number of years is t=10 so the future value is A=P(1+r/n)^n.t= 15000(1+0.06/12)^12.10= 27290.95$ With n is number payment period of the year GENERAL FOMULAR I=A-P SIMPLE INT: I=Prt A=P(1+rt) COMPOUND INT: A=P(1+i)^m=P(1+r/n)^nt with m=n.t *Find the interest rate for the given depositRead MoreMake Your Money Work For You - The Magic Of Compound Interest1163 Words   |  5 PagesYou - The Magic of Compound Interest By Maryanne Pope | Submitted On June 11, 2015 Recommend Article Article Comments Print Article Share this article on Facebook 1 Share this article on Twitter 6 Share this article on Google+ 2 Share this article on Linkedin 1 Share this article on StumbleUpon 1 Share this article on Delicious 1 Share this article on Digg 1 Share this article on Reddit 1 Share this article on Pinterest 1 Expert Author Maryanne Pope Compound interest is the eighth wonderRead MoreTime Value Of Money754 Words   |  3 Pagesreceive interest on the investment in the future. A dollar received today is worth more than a dollar promised sometime in the future. Interest is the payment for the use of the money lent or borrowed (principal). Interest is figured on a rate basis. Any amount of money invested is worth more the sooner it is received (Time Value of Money - TVM, 2013). Savings accounts draw interest on the balance of the account, usually for a years time. Suppose $100 is invested today at a 5% interest rate. AfterRead MoreThe Differences Between Stocks And Bonds1288 Words   |  6 Pagesfirst advantage is compound interest. â€Å"Compound interest is a miracle of the financial world. Compound interest, when given time, helps your money grow faster and faster† (learningmarkets.com, 2009, pg.1). According to Herbert Mayo (2012), the definition of interest that compounds is the â€Å"process by which interest is paid on interest that was previously earned† (pg. 106). A common example of this type of interest would be interest you would earn in a savings account. Generally, interest in a savings accountRead MoreCapital Budgeting Npv701 Words   |  3 Pagesfinite period of time at a given interest rate. Put another way, future value is the cash value of an investment at a particular time in the future. Start by considering the simplest case, a single-period investment. Investing For a Single Period: Suppose you invest $100 in a savings account that pays 10 percent interest per year. How much will you have in one year? You will have $110. This $110 is equal to your original principal of $100 plus $10 in interest. We say that $110 is the future value