14. a. You are planning your retirement and you come to theconclusion that you n
ID: 2770488 • Letter: 1
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14. a. You are planning your retirement and you come to theconclusion that you need to have saved $1,500,000 in 30 years. Youcan invest into an retirement account that guarantees you a 6%annual return. How much do you have to put into your account at theend of each year to reach your retirement goal? b. You set up a college fund in which you pay $2,000 each yearat the end of the year. How much money will you have accumulated inthe fund after 18 years, if your fund earns 7% compoundedannually? c. You are offered a security that will pay you $2,000 at theend of the year forever. If your discount rate is 8%, what is themost you are willing to pay for this security? d. What is the effective annual rate of 12% compoundedquarterly? e. You want to buy a new plasma television in 2years, when you think prices will have gone down to a morereasonable level. You anticipate that the television will cost you$2,400. If you can invest your money at 5% annual interest ratecompounded monthly, how much do you need to putaside today? 14. a. You are planning your retirement and you come to theconclusion that you need to have saved $1,500,000 in 30 years. Youcan invest into an retirement account that guarantees you a 6%annual return. How much do you have to put into your account at theend of each year to reach your retirement goal? b. You set up a college fund in which you pay $2,000 each yearat the end of the year. How much money will you have accumulated inthe fund after 18 years, if your fund earns 7% compoundedannually? c. You are offered a security that will pay you $2,000 at theend of the year forever. If your discount rate is 8%, what is themost you are willing to pay for this security? d. What is the effective annual rate of 12% compoundedquarterly? e. You want to buy a new plasma television in 2years, when you think prices will have gone down to a morereasonable level. You anticipate that the television will cost you$2,400. If you can invest your money at 5% annual interest ratecompounded monthly, how much do you need to putaside today?Explanation / Answer
(a) Future value of your savings amount(FV) = $1,500,000
Number of Years = 30 years
(b) Number of years (t) = 18 years
Interest rate(r) = 7%
Fundamount = $2,000
Future value of Annuity Factor = [Future value factor – 1]/ r
= [(1+r)t -1] / r
= [(1.07)18-1]/0.07
= 33.9990
Annuity future value = $2,000 * 33.9990
=$67,998
(c) Securities Cash flows for every year= $2,000
Interest rate ( r) = 8%
Present value = $2,000 / 0.08
=$25,000
(d) Effective Annual Rate = [1+(0.12 /12)]12-1
= (1.01)12-1
= 1.126825 – 1
= 0.126825 (or) 12.6825%
(e) Future Value = $2,400
Interest rate = 5% (compounded monthly)
Number of years = 2 years
Present Value = ?
Present Value = Future Value / (1+r)t
=$2,400 / (1+0.05/12)2*12
=$2,400 / 1.104765
=$2,172.40
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