How long will it take to have r30 000 for a trip to europe if i invest r20 000 now at 15% per year, compounded quarterly?

Compound  interest  formula

 

Where

A= Future value
P = the Principal (the initial amount of money) 
r = annual interest rate

t = time

n= number of times compounded in one t

Remark
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r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07..., 

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,

In our problem:

A= 30 000

P =20 000

r = 15%=0.15

time = t = ?

n= 4

applying the formula:







75% of 12 months is 3/4 of 12 months, which is 9 months

2 years, 9 months