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Chapter 8: Problem 67

A depositor opens a new savings account with \(\$ 6000\) at \(5 \%\) compounded semiannually. At the beginning of year 3 , an additional \(\$ 4000\) is deposited. At the end of six years, what is the balance in the account?

Short Answer

Expert verified
To obtain the balance in the account at the end of six years, perform the calculations in the previous steps. The answer will be the value obtained in Step 3.

Step by step solution

01

Calculate the balance for the first two years

Use the compound interest formula \(A = P(1 + r/n)^{nt}\), where 'P' is the principal amount (\$6000 in this case), 'r' is the annual interest rate (0.05), 'n' is the number of times that interest is compounded per year (2 for semiannual compounding), and 't' is the number of years the money is invested for (2). This gives: \(A = 6000(1 + 0.05/2)^{2*2}\).
02

Calculate the balance for the next four years

At the beginning of year 3, an additional \$4000 is deposited. Now 'P' is the sum of the balance at the end of year 2 and the addition deposit, i.e., 'P' is A + \$4000. Compute 'A' again but this time 't' is 4 years. So, we get: \(A = [A + 4000](1 + 0.05/2)^{2*4}\).
03

Compute the balances

Perform the calculations for the values of A obtained in steps 1 and 2 to get the balance on the account after six years.

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