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how long will it take for you to get $100,000.00 if you invest $5000.00 in an account giving you 9.7% interest, compound continuously?

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The formula for determining continously compounded interest is expressed as

A = Pe^rt

where

A is the amount in the account after t years

P is the principal or amuount invested

r is the interest rate

From the information given,

A = 100000

P = 5000

r = 9.7% = 9.7/100 = 0.097

By substituting these values into the formula, we have

100000 = 5000 e^0.97t

Dividing both sides of the equation, we have

100000/5000 = e^0.097t

20 = e^0.097t

We would take the natuaral log of both sides of the equation. it becomes

ln 20 = lne^0.097t

By applying the law of logarithm on the right side of the equation,

ln 20 = 0.097tlne

Recall, ln e = 1

Thus, we have

ln 20 = 0.097t

t = ln20/0.097

t = 30.9

It will take 30.9 years

User Niklas Heidloff
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