If Alexis invests $2,000 into a fund that earns 5.5% interest compounded annually, how long will it take for her investment to grow into $100,000?

Group of answer choices

About 62 years

About 58 years

About 73 years

About 108 years

About 73 years

Step-by-step explanation:

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 = 2000

r = 5.5% = 5.5/100 = 0.055

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

A = 100000

Therefore,.

100000 = 2000(1 + 0.055/1)^1 × t

100000/2000 = (1.055)^t

50 = 1.055^t

Taking log of both sides, it becomes

Log 50 = log 1.055^t

1.699 = t × log 1.055

1.699 = 0.0234t

t = 1.699/0.0234

t = 72.6

Approximately 73 years

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