Math Problem

Question

Suppose that you deposit $750 in a bank that offers an annual percentage rate of 4.0% compounded monthly.

a. What is your account balance after one year?
b. What is your account balance after 8 years?
c. What is the annual percentage yield for this account?

Answer 1

a.account balance after one year=$750[1+(0.04/12)]^12*1

                                               =$750[1+(1/300)]¹²

                                               =$750(301/300)¹²

                                               ≈$750*1.04

                                               ≈$780.56   

 

b.account balance after 8 years=$750[1+(0.04/12)]^12*8
                                             =$750[1+(1/300)]⁹⁶
                                             =$750(301/300)⁹⁶
                                             ≈$750*1.38
                                             ≈$1,032.30

 

c. the annual percentage yield for this account=[1+(0.04/12)]¹²-1
                                                                  =[(301/300)]¹²-1
                                                                  ≈1.0407-1
                                                                  ≈0.0407 or 4.07%

 

Answer 2

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

Where P = $ 750.  r = 4/100 = 0.04 ;  n = 12.

For t = 1 year, A = 750 x (1+0.04/12)¹² = 780.56  Account balance after 1 year = $ 780.56

 

 

For t = 8 years,  A= 750 x (1+0.04/12)^12x8 = 1032.29

 

Account balance after 8 years = $ 1032.29

 

Annual percent yield= (789.56 - 750)/750 x 100 = 5.27 %