Question

Find the amount that results from the given investment. $ 200 invested at 22​% compounded quarterly after a period of 3 years. After 3 ​years, the investment results in ​

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
----------------------------------------------------------------------------------

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,

-------------------------------------------------------------------------------------

Thus, in our problem, P=$200, r=22%=0.22, n=4, t=3

Applying the formula we have:


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


`A=200(1+ (0.22)/(4) )^(4\cdot3)=200(1+0.055)^(12)=200(1.055)^(12)=200\cdot 1.9`

=380 ($)


Answer: 380$