Roughly how many years would it take to turn 18750 into 2400

Roughly how many years would it take to turn $187.50 into $24,000 if you can invest the money at 7% per year, compounded annually?

Answer:

Compound Interest Formula:

A= P[1+r/n]^nt

Where A= Final Amount

P= Principal Amount

n= Number of times the interest is compounded per year

r=rate of interest

We have;

A= $24000

P= $187.5

n=1

r= 7%

24000= 187.5 [1+7/100]^t

128= [1.07]^t

[2]⁷ = [1.07]^t

Taking log on both the sides:

7 log(2)= t log(1.07)

t= 7 log(2)/log(1.07)

=[7 * 0.3010]/ 0.02938

= 2.107/0.02938

~ 72 Years

Hence it would take roughly 72 Years for $187.5 to become $24000!