Question

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 1

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

Step-by-step 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
`(1 + (r)/(100)) ^(n)`

a) Compounded Annually.

A = P
`(1 + (r)/(100)) ^(n)`

A = 8000
`(1 + (0.024)/(100)) ^(8)`

A = $9671.41

b) Compounded Monthly:

1 year = 12 months.

A = P
`(1 + (r)/(100*12)) ^(n*12)`

A = 8000
`(1 + (0.024)/(100*12)) ^(8*12)`

A = $9691.51

c) Compounded Weekly:

1 year = 52 weeks

A = P
`(1 + (r)/(100*52)) ^(n*52)`

A = 8000
`(1 + (0.024)/(100*52)) ^(8*52)`

A = $9692.93

d) Compounded Daily:

1 year = 365 days

A = P
`(1 + (r)/(100*365)) ^(n*365)`

A = 8000
`(1 + (0.024)/(100*365)) ^(8*365)`

A = $9693.30

e) Compounded Continuously:

For this we have following formula:

A = P
`e^{(n*r)/(100) }`

A = P
`e^{(8*0.024)/(100) }`

A = $9693.36