Assume that John deposits $8,000 into an account that has a 2.4% annual interest rate for 8 years. (a) If the interest is compounded annually, there will be $ in the account. (b) If the interest is compounded monthly, there will be $ in the account. (c) If the interest is compounded weekly, there will be $ in the account. (d) If the interest is compounded daily, there will be $ in the account. (e) If the interest is compounded continuously, there will be $ in the account.

Answer :

Answer:

a) Compounded Annually = $9671.41  

b) Compounded Monthly = $9691.51

c) Compounded Weekly = $9692.93  

d) Compounded Daily = $9693.30

e) Compounded Continuously = $9693.36  

Explanation:

Solution:

This question is very simple. We just need to know the basic formula.

Data Given:

P = Principal Amount = $8000

i = interest rate = 2.4% annual

n = period or year = 8 years.

So, our basic formula is:

A = P  [tex](1 + \frac{r}{100}) ^{n}[/tex]

a) Compounded Annually.

A = P  [tex](1 + \frac{r}{100}) ^{n}[/tex]

A = 8000 [tex](1 + \frac{0.024}{100}) ^{8}[/tex]

A = $9671.41  

b) Compounded Monthly:

1 year = 12 months.

A = P  [tex](1 + \frac{r}{100*12}) ^{n*12}[/tex]

A = 8000  [tex](1 + \frac{0.024}{100*12}) ^{8*12}[/tex]

A = $9691.51

c) Compounded Weekly:

1 year = 52 weeks

A = P  [tex](1 + \frac{r}{100*52}) ^{n*52}[/tex]

A = 8000  [tex](1 + \frac{0.024}{100*52}) ^{8*52}[/tex]

A = $9692.93

d) Compounded Daily:

1 year = 365 days

A = P  [tex](1 + \frac{r}{100*365}) ^{n*365}[/tex]

A = 8000  [tex](1 + \frac{0.024}{100*365}) ^{8*365}[/tex]

A = $9693.30

e) Compounded Continuously:

For this we have following formula:

A = P[tex]e^{\frac{n*r}{100} }[/tex]

A = P[tex]e^{\frac{8*0.024}{100} }[/tex]

A = $9693.36