Problem

Use the appropriate compound interest formula to find the amount that will be in each account, given the stated conditions.
$\$ 39,000$ invested at $2 \%$ annual interest for 7 years compounded (a) annually; (b) semiannually
(a) If the interest is compounded annually, there will be $\$ \square$ in the account after 7 years.
(Do not round until the final answer. Then round to the nearest cent as needed.)

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{\$44,798.74}\) is the final amount in the account after 7 years if the interest is compounded annually.

Steps

Step 1 :Given that the principal amount (P) is $39,000, the annual interest rate (r) is 2% or 0.02 in decimal, the number of times that interest is compounded per year (n) is 1 (since it's compounded annually), and the time the money is invested for in years (t) is 7 years.

Step 2 :We can use the compound interest formula A = P(1 + r/n)^(nt) to find the amount in the account after 7 years.

Step 3 :Substitute the given values into the formula: A = 39000(1 + 0.02/1)^(1*7)

Step 4 :Solving the equation gives A = 44798.741038321925

Step 5 :Rounding to the nearest cent gives the final amount in the account after 7 years as $44,798.74

Step 6 :\(\boxed{\$44,798.74}\) is the final amount in the account after 7 years if the interest is compounded annually.

link_gpt