Question

Riverside Bank offers to lend $50K at a nominal rate of 6.5%, compounded monthly. The loan must be repaid at the end of the year. Midwest Bank also offers to lend you the $50K, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?

Answer 1

Conditions

Riverside Bank offers to lend $50K at a nominal rate of 6.5%, compounded monthly. The loan must be repaid at the end of the year. Midwest Bank also offers to lend you the $50K, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?

Solution

Here we must compare 2 cash flows.

The future value of money we must pay to Riverside Bank (RB) is:

$$50000\$ \cdot \left(1 + \frac{0.065}{12}\right)^{12} = 53348.6\$$$

The future value of money we must pay to Midwest Bank (MB) is:

$$50000\$ \cdot (1 + 0.07) = 53500\$$$

So, we can see, that RB is better to lend, than MB.

The effective annual rate could be found by using the following formula:

$$r = (1 + i/n)^n - 1$$ $$r_{RB} = \left(1 + \frac{0.065}{12}\right)^{12} - 1 = 0.06697$$ $$r_{MB} = 0.07$$

We can make a conclusion, that the effective annual rate of RB is lower than MB's on $0.07 - 0.06697 = 0.00303$ (approximately $0.3\%$)