I Need Help answering questions 1 and 2 Can I have some help

I Need Help answering questions 1 and 2. Can I have some help?

Department of Mathematics East Stroudsburg University Math 135: Pre-Calculus Homework 2: Exponential and Logarithmic Functions Due November 20, 2017 This is a graded homework assignment. You may work on this assignment with a partner and turn in one solution for the two of you. (Put both names on the paper.) Please do not ask a tutor or anyone outside this class for help with this assignment. Of course, you may ask me for help. (I am a part of this class.) Please write your answers on a separate sheet and include your work. Please be as neat as possible. Please use complete sentences when answering the questions 1) (40 points) If you invested S1,000 in an account paying an annual percentage rate compounded quarterly, and you wanted to have $2,500 in your account at the end of your investment time, what interest rate would you need if the investment time were 1 year, 10 years, 20 years, 100 years? What if the interest is compounded continuously, instead of quarterly? 2) (40 points) There is a relationship between the mortgage amount, the number of payments, the amount of the payment, how often the payment is made, and the interest rate. The following formulas illustrate the relationshijp where P the payment, r = the annual rate, M = the mortgage amount. the number of years, and n the number of payments per year

Solution

multiple questions posted.please post each question seperately.only first question in list will be answered

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1)

principle amount P=1000, rate of interest =r , accumulated amount A=2500

when compunded quarterly:

A=P(1+(r_/n))^nt

n=4

i) investment time is1 year:

t=1

=>2500=1000(1+(r_/4))^4*1

=>(1+(r_/4))⁴=2.5

=>r=4(2.5^1/4-1)

=>r=1.02973372

=>r=102.973372%

intereste rate needed = 102.97% approximately

ii)

investment time is10 years:

t=10

=>2500=1000(1+(r_/4))^4*10

=>r=4(2.5^1/40-1)

=>r= 0.09268661879087059

=>r=9.27% approximately

iii)

investment time is20 years:

t=20

=>2500=1000(1+(r_/4))^4*20

=>r=4(2.5^1/80-1)

=>r=  0.0460779

=>r=4.61% approximately

iii)

investment time is 100 years:

t=100

=>2500=1000(1+(r_/4))^4*100

=>r=4(2.5^1/400-1)

=>r=   0.009173410195767673

=>r=0.92% approximately

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when compunded continously:

A=Pe^rt

i)

investment time is1 year:

t=1

=>2500=1000*e^r*1

=>r=(1_/1)ln(2.5)

=>r=0.91629073187415506518352721176801

=>r=91.63% approximately

ii)

investment time is 10 years:

t=10

=>2500=1000*e^r*10

=>r=(1_/10)ln(2.5)

=>r=0.091629073187415521

=>r=9.16% approximately

iii)

investment time is 20 years:

t=20

=>2500=1000*e^r*20

=>r=(1_/20)ln(2.5)

=>r=0.04581453659370776

=>r=4.58% approximately

iv)

investment time is 100 years:

t=100

=>2500=1000*e^r*100

=>r=(1_/100)ln(2.5)

=>r=0.0091629073187415521

=>r=0.916% approximately