Calculating compound interest

Question

Heather received $100 for her 13th birthday. If she saves it in a bank with 3% interest compounded quarterly, how much money will she have in the bank by her 16th birthday?

 

 

 

 

 

Answer 1

Use the compound interest formula A=P(1+(r/n))^nt, where r=annual interest rate, n=number of interest payments per year, and t=number of years.

P=the principle, or the amount initially invested.  A= the value after time t

For this problem r=0.03, n=4, and t=3.

A = 100(1+(.03/4))⁴⁽³⁾ = 100(1.0075)¹²= 100(1.0938) = $109.38

Answer 2

Recall the formula for compound interest is as follows:

          A  =  P·(1  +  r/n)^nt ,   where

     P = principal amount (initial amount deposited)

      r = annual rate of interest (in decimal form)

      t = # of years amount is deposited for

     n = # of times interest is compounded per year

     A = amount accumulated after t years, including interest

The problem asks how much money Heather will have in the bank by her 16th birthday when she deposited $100 on her 13th birthday in a bank with 3% interest compounded quarterly. From this, we have the following information:

     P = $100

     r = 0.03     ==>     3%/100% = 0.03 

     t = 3 years     ==>     16 - 13 = 3

     n = 4     ==>     since there are 12 months per year and 12/4 = 3 months,

                 then interest is compounded  every 3 months which is a total of 4 times per year

Therefore, 

          A = P(1 + r/n)^nt

             = 100(1 + 0.03/4)^4·3

             = 100(1 + 0.0075)¹²

             = 100(1.0075)¹²

             = 109.38069

             ≈ 109.38

Thus, Heather will have $109.38 in the bank by her 16th birthday