Question

1. A bank account pays 0.5% monthly interest.a. If $600 is put in the account, what will the balance be at the end of one year, assuming no additionaldeposits or withdrawals are made?b. What is the effective annual interest rate?c. Is the effective annual interest rate more or less than 6% (the nominal interest rate)?

Answer 1

a. 637.007$

b. 0.5%

c. Less than the nominal interest rate

Explanation & Steps:

a.

$600\cdot(1.005)^{12}\text{ }\cong637.006687\text{ }\cong\text{ 637.007\ }$

b.

$\begin{gathered} (1+(\frac{0.5\%}{12}))^{12}\text{ - 1 = x} \\ (1\text{ + (}\frac{0.005}{12}))^{12}\text{ - 1 = x} \\ (1+0.000417)^{12}-1\text{ = x} \\ (1.000417)^{12}\text{ - 1 = x} \\ 1.000502\text{ - 1 =x} \\ 0.00502\text{ = }0.5\text{ = x} \end{gathered}$

c. 0.5% < 6%