# 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?

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

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

Yadkin’s the better choice

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)