An investment of $75,000 increases at a rate of 12.5% per year.

A) What is the value of the investment after 30 years if the interest is compounded yearly?

B) What is the value of the investment after 30 years if the interest is compounded continuously?

(I need B for that most part)

Step-by-step explanation:

A) We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $75000

r = 12.5% = 12.5/100 = 0.125

n = 1 because it was compounded once in a year.

t = 30 years

Therefore,

A = 75000 (1 + 0.125/1) ^1 * 30

A = 75000 (1.125) ^30

A = $2568248

The formula for continuously compounded interest is

A = P x e (r x t)

Substituting the above information, it becomes

A = 75000 x e^ (0.125 x 30)

A = 75000 x e^ (3.75)

A = $3189081