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Assignment: Compound Interest Investigation

Tyler has earned money by helping out on a neighbor's farm and now wants to put his earnings in a savings account. He is a bit confused on the different interest options available and how each will impact the amount he has after several years. Help Tyler better understand by showing him how his money will increase in an account that uses simple interest and one that uses compound interest over a specified period of time.

1. a. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% interest compounded annually, how much will he have in his account after 5 years?


Year

Principal

Principal + Compound Interest

1

$1500



2



3



4



5




b. If Tyler deposits $1500 of the $3200 he has earned in an account that pays 4% simple interest, how much will he have after 5 years? Show all work.








c. Which account would yield a greater amount? What is the difference between the two amounts?







2. a. If Tyler deposits $2000 of the $3200 he has earned in an account that pays 8% interest compounded quarterly, how much will he have in his account after 1 year?


Quarter

Principal

Principal + Compound Interest

1

$2000



2



3



4




b. If Tyler deposits $2000 of the $3200 he has earned in an account that pays 8% simple interest, how much will he have after 1 year? Show all work.















c. Which account would yield a greater amount? What is the difference between the two amounts?













3. Tyler decides to deposit his earnings of $3200 in a savings account. Bank A offers an account with a simple interest rate of 3.5%. Bank B offers an interest rate of 3.4% compounded annually. After 3 years, in which bank will Tyler have the greatest total? Show all work.

a. Find the interest earned for Bank A.










b. Find the total amount for Bank B.




c. Which bank should Tyler choose if he wants to earn the greater amount? Explain your reasoning.





d. Which account would yield a greater amount? What is the difference between the two amounts?

Respuesta :

1)

a)

P = 1500, r = 4% = 0.04, n = 5

[tex] A = 1500 (1+0.04)^5= 1824.98 [/tex]

He shall have $1824.98 in his account after 5 years

b)

Here P = 1500 , r = 4% = 0.04, n = 5 but simple interest

So

[tex] I=PRn= 1500(.04)(5)=300 [/tex]

Interest = $300

Amount in his account after 5 years = 1500 + 300 = $1800

c)

First one shall yield a better income and by 1824.98-1800 = $24.98

2)

a)

P= $2000, r = 8% = 0.08 so quaterly = 0.08/4 = 0.02, n = 1 year

[tex] A = P(1+r)^{4n}  =2000(1+0.02)^4 =2164.86 [/tex]

There shall be $2164.86 after 1 year

b)

P = 2000, r= 8%=0.08 and n = 1 for simple interest

[tex] I=PRn = 2000(0.08)(1)=160 [/tex]

Amount after 1 year shall be 2000 + 160= $2160

c)

First option is a better option.

The difference is 2164.86 - 2160 = $4.86

3)

a)

Bank A

P= 3200, r = 3.5%= 0.035, n = 3 years for simple interest

[tex] I =3200(0.035)(3)=336  [/tex]

Interest earned in Bank A = $336

b)

Bank B

P = 3200, r = 3.4% = 0.034, n= 3

[tex] A= P(1+r)^n=3200(1+0.034)^3=3537.62 [/tex]

Interest earned = 3537.62 - 3200 = $337.62

c)

Tyler must choose Bank B as it fetches greater interest

d)

The difference in interest = 337.62 - 336 = $1.62


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