Question

If Siddiq invests $10,000 into a fund that earns 8% interest compounded annually, how long will it take for his investment to grow into $100,000?
About 25 years

About 30 years

About 40 years

About 35 years

Answer 1

Answer: About 30 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 = 10000

r = 8% = 8/100 = 0.08

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

A = 100000

Therefore,

100000 = 10000(1+0.08/1)^1 × t

100000/10000 = (1.08)^t

10 = (1.08)^t

Taking log to base 10 of both sides, it becomes

Log 10 = log 1.08^t

1 = t × log 1.08 = 0.03342t

t = 1/0.03342

t = 29.9

Approximately 30 years