Question

Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is (use the tables in the handbook):

Answer 1

Answer:$119,735.6

Explanation:

To calculate the total in the account,we use the compound interest formula

A= P ( 1+ ( R/2)/100)∧2n

P = $ 12,000 n = 4 R = 12%

A = 12,000 (1+(12/2/100)∧2*4

A = 12,000 ( 1+ ( 6)/100)∧2*4

A = 12,000 ( 1+0.06)∧8

A= 12,000 ( 1.06)∧8

A = 12,000 ( 1.5938)

A= 12,000* 1.5938

A= $ 19,125.6

Another deposit into the account

A = P ( 1+(R/2)/100)∧2n

A= 50,000 (1+12/2/100)∧2*6

A= 50,000 (1+6/100∧12

A = 50,000 ( 1+0.06)∧12

A = 50,000 (1.06)∧12

A= 50,000 ( 2.0122)

A = 50,000* 2.0122

A = 100,610

Therefore, the total in the account

$19,125.6 + $100,610

= $119,735.6