compund value

Question

Complete the following using compound future value (Please use only the following provided Table). (Round your final answers to 2 decimal places. Omit the "$" sign in your response.)

Time is 5 years

Prinicpal is 3,400

Intrest rate is 12%

It is Compounded  Semiannually

what is the amount?

what is the interest?

 

 

Answer 1

The formula for annual compound interest is A=P(1+r/n)^nt where:

A = final amount

P = principal amount (initial investment)

r = annual nominal interest rate (as a decimal, not in percentage)

n = number of times the interest is compounded per year

t = number of years

In your problem we have P=3400, r=0.12, n=2, t=5, so we just need to plug these values in:

A = 3400*(1+0.12/2)^2*5 = 3400*1.06¹⁰ = 6088.882168245702313984 which rounds to 6088.88 for the final balance.

The total interest is 6088.88-3400 = 2688.88

Answer 2

First thing you want to do is write down the equation your going to use for Feature Value, 

A = P ( 1 + r/n )^nt  were P= principle , r= intrest Rate , n= # times per year, t= total time, and A your Feature Amount. 

There fore     A = 3,400 ( 1 + .12/2)²⁽⁵⁾ by substituting all the given values.  

Notice that The Rate of 12% became .12 by dividing 12/100, This is due to the fact that the percentage value can not be use to simplify the problem , Therefore it needs to be converted to a decimal value. 

Also your "n" value is 2, since its compounded semiannually, every 6 months, which means 2 times a year. 

The Algebra part can be confusing at times... Take it step by step

1.   ( 1 + .12/2) = ( 1 + .06) = 1.06

2.   (1.06)²⁽⁵⁾ = (1.06)¹⁰ = 1.7908477

3.  3,400 * ( 1.7908477) = 6088.88218 

4.  A = $ 6088.88