Comparing Two Alternatives Suppose that April has access to an investment that will pay 10% interest compounded continuously. Which is better: to be given $1000 now so that she can take advantage of this investment opportunity or to be given $1325 after 3 years?

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.4: Mathematics Of Finance
Problem 2E
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SECTION 4.7 Financial Models 347
51. Comparing IRA Investments Will invests $2000 in his
IRA in a bond trust that pays 9% interest compounded
semiannually. His friend Henry invests $2000 in his IRA
in a certificate of deposit that pays 8% compounded
continuously. Who has more money after 20 years, Will or
Henry?
52. Comparing Two Alternatives Suppose that April has access
to an investment that will pay 10% interest compounded
continuously. Which is better: to be given $1000 now so that
she can take advantage of this investment opportunity or to
be given $1325 after 3 years?
53. College Costs The average annual cost of college at 4-year
private colleges was $29,056 in the 2012-2013 academic
year. This was a 4.2% increase from the previous year.
Source: The College Board
(a) If the cost of college increases by 4.2% each year, what
will be the average cost of college at a 4-year private
college for the 2030-2031 academic year?
(b) College savings plans, such as a 529 plan, allow
individuals to put money aside now to help pay for
college later. If one such plan offers a rate of 4%
compounded continuously, how much should be put in a
college savings plan in 2015 to pay for 1 year of the cost
of college at a 4-year private college for an incoming
freshman in 2030?
54. Analyzing Interest Rates on a Mortgage Colleen and Bill
have just purchased a house for $650,000, with the seller
holding a second mortgage of $100,000. They promise to
pay the seller $100,000 plus all accrued interest 5 years from
now. The seller offers them three interest options on the
second mortgage:
(a) Simple interest at 12% per annum
Transcribed Image Text:s $100 to w long will ontinuous, 0 to invest g will it be uous, how -ars will it $25,000? tinuously. ars will it $80,000? tinuously. $90,000 preciation mpounded ges 1.25% ith charge customer ns. What is or $15,000 arents for ntinuously, ths to pay he has the n account ths he will SECTION 4.7 Financial Models 347 51. Comparing IRA Investments Will invests $2000 in his IRA in a bond trust that pays 9% interest compounded semiannually. His friend Henry invests $2000 in his IRA in a certificate of deposit that pays 8% compounded continuously. Who has more money after 20 years, Will or Henry? 52. Comparing Two Alternatives Suppose that April has access to an investment that will pay 10% interest compounded continuously. Which is better: to be given $1000 now so that she can take advantage of this investment opportunity or to be given $1325 after 3 years? 53. College Costs The average annual cost of college at 4-year private colleges was $29,056 in the 2012-2013 academic year. This was a 4.2% increase from the previous year. Source: The College Board (a) If the cost of college increases by 4.2% each year, what will be the average cost of college at a 4-year private college for the 2030-2031 academic year? (b) College savings plans, such as a 529 plan, allow individuals to put money aside now to help pay for college later. If one such plan offers a rate of 4% compounded continuously, how much should be put in a college savings plan in 2015 to pay for 1 year of the cost of college at a 4-year private college for an incoming freshman in 2030? 54. Analyzing Interest Rates on a Mortgage Colleen and Bill have just purchased a house for $650,000, with the seller holding a second mortgage of $100,000. They promise to pay the seller $100,000 plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage: (a) Simple interest at 12% per annum
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