Riverside bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. the loan (principal plus interest) must be repaid at the end of the year. midwest bank also offers to lend you the $50,000, but it will charge an annual rate of 6.2%, 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

The effective annual rate of Midwest is 0.2% lower than the rate charged by Riverside.

Further Explanation:

Riverside Bank:

Principal = $50,000

Duration = 1 year

APR = 6.5%

The amount paid after 1 year is

A = 50000(1 + 0.065/12)¹² = $53,348.59

Midwest Bank:

Principal = $50,000

APR = 6.2%

Duration = 1 year

The amount paid after 1 year is

A = 50000*(1 + 0.062) = $53,100.00

The amount charged by Midwest is lower:

Let r = the effective annual rate of Riverside Bank.

Then

50000*(1 + r) = 53348.59

1 + r = 53348.59/50000 = 1.067

r = 0.067 = 6.7%

Effective annual rate:  

The viable yearly financing cost is the loan fee that is really earned or paid on a venture, advance or other money related item because of the aftereffect of intensifying over a given timeframe. It is additionally called the powerful loan cost, the viable rate or the yearly comparable rate.  

Instructions to Calculate the Effective annual Rate:  

1.Determine the expressed loan fee. The expressed financing cost (additionally called yearly rate or ostensible rate) is generally found in the features of the credit or store understanding.

2.Determine the quantity of aggravating periods.  

3.Apply the EAR Formula: EAR = (1+ I/n)n – 1.

Subject: mathematics

Level: college

Keywords: Riverside Bank, Midwest Bank, The amount charged by Midwest is lower, Effective annual rate, Instructions to Calculate the Effective annual Rate.

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