$1000 invested at 5% compounded semiannually after 8 years

Question

i have no idea how to do this. please help!

Answer 1

The equation you should use to answer this problem is A = P(1 + (r/n))^n*t, where

A = final amount

P = initial amount

r = rate

n = number of times the amount is compounded per year, and

t = number of years

 

All the variables are given to solve for A. The initial investment is $1000, the rate is 5% (but must be in decimal form: 0.05), the number of times the investment is compounded is 2 (because semiannually means twice a year), and time passed is 8 years.

 

The equation will look like this:

 

A = 1000(1 + (0.05/2))^2*8

 

The steps to solve are as follows:

 

Simplify within the parentheses first.

A = 1000(1.025)¹⁶

 

Raise the value within the parentheses to the exponent.

A = 1000(1.485)

 

And finally multiply to get the final answer of:

A = $1484.51