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If Debbie starts a retirement account with $100 that has an annual rate of return of 8%, how long (in years) would it take for her to
have at least $100,000 if interest is compounded continuously?
A) 1 year
B) 8 years
C) 87 years
D) 90 years

Respuesta :

Answer:

C.) 87 years

Step-by-step explanation:

I've taken the test! Hope this helps! ;)

MrRoyal

The number of years for her to have at least $100,000 if interest is compounded continuously is 90

How to determine the number of years?

The given parameters are:

Amount, A = 100,000

Principal, P = 100

Rate, r = 8%

Amount is calculated using:

A = P * (1 + r)^t

So, we have:

100000 = 100 * (1 + 8%)^t

Divide by 100

1000 = (1 + 8%)^t

Evaluate the sum

1000 = 1.08^t

Take the logarithm of both sides

log(1000) = log(1.08)^t

Apply the law of logarithm

log(1000) = tlog(1.08)

Solve for t

t = log(1000)/log(1.08)

Divide

t = 89.7

Approximate

t = 90

Hence, the number of years is 90

Read more about compound interest at:

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