Question

50 POINTS!!!

Math...Money...Interest...
Please give the correct answers and show the steps. I will report your account if I find an error. Thank you for your help.

Answer 1

2.

Quarterly:

• 100000 = 60000(1 + 0.075/4)^4t
• t ≈ 6.87466382 years

Monthly:

• 100000 = 60000(1 + 0.075/12)^12t

• t ≈ 6.83227061 years

Continuously:

• 100000 = 60000e^0.075t
• t ≈ 6.811008 years

3.

Twice a year:

• 300 = 100(1 + 0.1025/2)^2t
• t ≈ 10.99053398 years

Eight times a year:

• 300 = 100(1 + 0.1025/8)^8t
• t ≈ 10.78668624 years

Continuously:

• 300 = 100e^0.1025t
• t ≈ 10.718169 years

Explanation:

The formula for compound interest is:

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

The formula for compounded continuously is:
A = Pe^rt

Where:

A = the future value of the investment

P = the principal balance

r = the annual interest rate (decimal)

n = number of times interest is compounded per year

t = the time in years

Using that we can plug the formula in for each question:

2.

Quarterly:

• 100000 = 60000(1 + 0.075/4)^4t
• Compounded quarterly means in a year, it is compounded 4 times
• Note that the question is asking to find how much time it takes so t is the thing we need to solve for
• t ≈ 6.87466382 years

Monthly:

• 100000 = 60000(1 + 0.075/12)^12t

• t ≈ 6.83227061 years

Continuously:

• 100000 = 60000e^0.075t
• We are now using the compounded continuous formula
• t ≈ 6.811008 years

3.

Twice a year:

• Since the question does not give us a starting amount but it gives us a goal of tripling the money, we can substitute any amount of money for P and A as three times P
• For now, let's say P is 100 and A is 3 times 100 so A is 300
• 300 = 100(1 + 0.1025/2)^2t
• t ≈ 10.99053398 years

Eight times a year:

• We will continue to place hold P as 100 and A as 300
• 300 = 100(1 + 0.1025/8)^8t
• t ≈ 10.78668624 years

Continuously:

• We will now use the compounded continuous formula
• 300 = 100e^0.1025t
• t ≈ 10.718169 years