Question

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?

Answer 1

Compound interest formula

`A=P(1+ (r)/(n) )^(nt)`

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:


`A=P(1+ (r)/(n) )^(nt)\\\\30,000=20,000(1+ (0.15)/(4) )^(4t)\\\\ \displaystyle{(30,000)/(20,000) =(1.0375)^(4t)`


`\displaystyle{ 1.5={(1.0375^4)}^t\\\\`


`1.5=1.159^t\\\\ \displaystyle { t=log_(1.159)1.5=2.75`

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

Answer: 2 years, 9 months