# How much more money per year in interest did their investment draw at the bank with the better deal?

Deal Score0

Mrs. Griswoldâ€™s father gave Mr. Griswold a dowry of \$ 15,000 when he and Mrs. Griswold got married. They decided to put that money into a savings account and eventually use it for a down payment on a house. In their search for the best deal, they found two promising accounts at two different banks. Yadkin Valley Bank and Trust offered a 5.4% interest rate compounded monthly while, Wachovia Bank offered a 5.385% interest rate compounded continually.

Which bank had the best deal?

Catenary
February 13, 2011 at 7:23 am

(1+0.054/12)^12 = 1.0554 (5.54% effective yield)

(1+0.05385/10000)^10000 = 1.05533 (5.53% effective yield)

math guy
February 13, 2011 at 8:08 am

After the first year, the balance at Yadkin Valley Bank would be:
B = 15000(1+0.054/12)^12
B = 15000(1+0.0045)^12
B = 15000(1.0045)^12
B = 15830.35, so the interest is \$ 830.35.

AT Wachovia Bank, the balance would be

B = 15000* e^(0.05385*1)
B = 15829.89, so the interest would be \$ 829.89

So Yadkin Valley Bank will pay them \$ 0.46 more.

Edit:
Rather than using continuous compounding, Catenary is approximating it (rather well) by compounding the interest some 10000 times during the year. However, if this is for school, I suggest that you use the formula:
Balance = principal * e^(rate*time)

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