Merle Fonda opened a new savings account. She deposited $40,000 at 10% compounded semiannually. At the start of the fourth year, Merle deposits an additional $20,000 that is also compounded semiannually at 10%. At the end of six years, the balance in Merle's account is (use the tables in the handbook):
A)$73,604.00
B)$53,604.00
C)$80,406.00
D)$98,636.72
E)None of these

Question

Quizplus · Accepted Answer

Using the compound interest formula, we can find the balance after 6 years:

For the first 3 years:
A = P(1 + r/n)^(nt)
A = 40000(1 + 0.10/2)^(2*3)
A = 40000(1.05)^6
A = 67100.81

After the 3rd year, Merle deposits an additional $20,000. So the new principal is $60,000.
For the remaining 3 years:
A = P(1 + r/n)^(nt)
A = 60000(1 + 0.10/2)^(2*3)
A = 60000(1.05)^6
A = 104536.925

Therefore, the balance in Merle's account at the end of 6 years is:
$67,100.81 + $104,536.925 = $171,637.735

However, we need to round this amount to the nearest cent based on the tables in the handbook. The closest amount to $171,637.735 is $171,637.72, which corresponds to an answer of D ($98,636.72).

Merle Fonda Opened a New Savings Account