Question

What are the future value and the interest earned if $3200 is invested for 3 years at 8% compounded quarterly? (Round your answers to the nearest cent.)

Answer 1

$4058.37

Explanation:

If we use the equation
`A=P(1+(r)/(n))^(t*n)`

A= the total Amount

P= principal/original amount = $3200

r= rate = 8% or 0.08

n= number of times compounded a year = quarter = 4

t= time = 3 years

You plug it into the equation

`A=3200(1+(0.08)/(4))^(3*4)`

`3200(1+0.02)^(12) \\3200(1.02)^(12)\\3200(1.26824179456)\\4058.37`

Answer 2

Future Value (FV) = Principal (P) * (1 + (r/n))^(n*t)

Where:
P = $3200 (principal)
r = 8% (interest rate)
n = 4 (number of times compounded per year)
t = 3 years (time)

Plugging in the values, we have:

FV = $3200 * (1 + (0.08/4))^(4*3)

Calculating this, we find that the future value (rounded to the nearest cent) is $3815.35.

To find the interest earned, we subtract the principal from the future value:

Interest Earned = FV - P = $3815.35 - $3200 = $615.35.

Therefore, the future value is approximately $3815.35 and the interest earned is approximately $615.35.